numerical analysis and computing of free boundary problems for concrete carbonation chemical corrosion abstract this paper deals with the construction analysis and computation of a numerical method to solve a moving boundary coupled nonlinear system of parabolic reaction diffusion equations arising in concrete carbonation problems by means of a front fixing transformation the domain of the problem becomes fixed and the position of the moving carbonation front has to be determined together with the mass concentrations of the involved chemical species qualitative properties like positivity and stability of the numerical solution are established spatial monotone behaviour of the solution is also proved numerical examples illustrate these results

synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

statistical analysis of airport network of china through the study of airport network of china anc composed of 128 airports nodes and 1165 flights edges we show the topological structure of anc conveys two characteristics of small worlds a short average path length 2 067 and a high degree of clustering 0 733 the cumulative degree distributions of both directed and undirected anc obey two regime power laws with different exponents i e the so called double pareto law in degrees and out degrees of each airport have positive correlations whereas the undirected degrees of adjacent airports have significant linear anticorrelations it is demonstrated both weekly and daily cumulative distributions of flight weights frequencies of anc have power law tails besides the weight of any given flight is proportional to the degrees of both airports at the two ends of that flight it is also shown the diameter of each subcluster consisting of an airport and all those airports to which it is linked is inversely proportional to its density of connectivity efficiency of anc and of its subclusters is measured through a simple definition in terms of that the efficiency of anc s subclusters increases as the density of connectivity does anc is found to have an efficiency of 0 484

synchronization in dynamic networks with nonsymmetrical time delay coupling based on linear feedback controllers based on a general complex dynamic network model with nonsymmetrical time delay coupling and without assuming irreducibility a strategy for global exponential synchronization is proposed based on the approach of linear state feedback controllers especially the criteria for controller design can be expressed by inequalities instead of matrix inequalities thus the proposed controllers can be easily constructed without relying on any numerical toolbox the efficiency of the control scheme is revealed by simulations on a network consisting of the unified chaotic systems with nearest neighbour unidirectional time delay coupling

synchronization in weighted scale free networks with degree degree correlation abstract we study synchronization phenomena in scale free networks of asymmetrically coupled dynamical systems featuring degree degree correlation in the topology of the connection wiring we show that when the interaction is dominant from the high degree to the low degree or from the low degree to the high degree nodes synchronization is enhanced for assortative or disassortative degree degree correlations

pinning control of complex dynamical networks with general topology abstract recently the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes e g symmetric coupling uniform coupling and linear coupling however most real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper pinning control of a continuous time complex dynamical network with general coupling topologies is studied some generic stability criteria based on master stability function msf are derived for such a general controlled network which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes then these results are extended to discrete time case previous results about symmetric uniform or linear coupled networks in this area are included as special cases of the present work numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification

synchronizability of complex networks recent interest in the study of networks associated with complex systems has led to a better understanding of the factors and parameters relating the topology of the associated networks with the dynamics of the systems and in particular their synchronization in this paper by using known and new results from spectral graph theory we characterize relevant factors which affect the synchronization of complex networks

probabilistic synchronisation of pinning control this paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty a probabilistic control method for adaptive synchronization is presented all required probabilistic models of the network are assumed to be unknown therefore estimated to be dependent on the connectivity strength the state and control values robustness of the probabilistic controller is proved via the liapunov method furthermore based on the residual error of the network states we introduce the definition of stochastic pinning controllability a coupled map lattice with spatiotemporal chaos is taken as an example to illustrate all theoretical developments the theoretical derivation is complemented by its validation on two representative examples

lmi based criteria for synchronization of complex dynamical networks this paper considers the problem of controlling a complex dynamical network by means of pinning we point out that the synchronization criterion given in the form of matrix eigenvalues can be equivalent to a linear matrix inequality criterion we further investigate network synchronization via pinning and prove several linear matrix inequality theorems in particular we theoretically provide two typical pinning strategies based on whether the graph which is made up of unpinned nodes and edges between them is irreducible or not numerical simulations including k regular networks star shaped networks and ba scale free networks are shown for illustration and verification

distributed static output feedback control for state synchronization in networks of identical lti systems this paper studies state synchronization of multi agent systems with disturbances using distributed static output feedback opfb control the bounded l 2 gain synchronization problem using distributed static opfb is defined and solved the availability of only output measurements restricts the local controls design while the communication graph topology restricts global information flow among the agents it is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded l 2 gain static opfb one condition is on the output measurement matrix on a local scale and the other on the graph laplacian matrix on a global scale under additional conditions a distributed two player zero sum game using static opfb is also solved and leads to distributed nash equilibrium on the communication graph as a special case the static opfb globally optimal control is given a new class of digraphs satisfying the above condition on the graph laplacian is studied the synchronizing region for distributed static opfb control is exposed and found to be conical different than the infinite right half plane synchronizing region for distributed state feedback

optimizing the controllability of arbitrary networks with genetic algorithm abstract recently as the controllability of complex networks attracts much attention how to optimize networks controllability has become a common and urgent problem in this paper we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under popov belevitch hautus rank condition the experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured furthermore we explore how network structure affects its controllability and find that the sparser a network is the more control nodes are needed to control it and the larger the differences between node degrees the more control nodes are needed to achieve the full control our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations

brief paper global stabilization of complex networks with digraph topologies via a local pinning algorithm this paper concerns the global stability of controlling a complex network with digraph topology to a homogeneous trajectory of the uncoupled system by the local pinning control algorithm the derived stability condition indicates that the smallest real part of eigenvalues of the laplacian sub matrix corresponding to the unpinned vertices can be used to measure the stabilizability of a digraph with a given pinned vertex set a pinned vertex set can stabilize a directed network to some unstable trajectories for instance to a chaotic trajectory of the uncoupled systems if and only if the pinned vertex set can access all other vertices in the digraph furthermore in the bigraph case the analytical estimation of the stabilizability s lower bound suggests that an optimal pinning strategy should take not only the vertex degree but also the shortest path between pairs of vertices into considerations

adaptive pinning control for the projective synchronization of drive response dynamical networks abstract this paper studies the projective synchronization of a drive response dynamical network of partially linear systems the coupling configuration matrix of the network is not necessarily symmetric two adaptive pinning control strategies are derived based on the barbalat s lemma in the first control strategy the pinning control gain is adaptively updated to realize the projective synchronization in the second control strategy both the pinning control gain and the coupling strength between nodes are adaptively updated numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network

synchronization based topology identification of weighted general complex dynamical networks with time varying coupling delay abstract many existing papers investigated the geometric features control and synchronization of complex dynamical networks provided with certain topology however the exact topology of a network is sometimes unknown or uncertain based on lasalle s invariance principle we propose an adaptive feedback technique to identify the exact topology of a weighted general complex dynamical network model with time varying coupling delay by receiving the network nodes evolution the topology of such a kind of network with identical or different nodes or even with varying topology can be monitored in comparison with previous methods time delay is taken into account in this simple analytical and systematic synchronization based technique particularly the weight configuration matrix is not necessarily symmetric or irreducible and the inner coupling matrix need not be symmetric illustrative simulations are provided to verify the correctness and effectiveness of the proposed scheme

bounds on the smallest eigenvalue of a pinned laplacian matrix in this note we study a networked system with single multiple pinning given a weighted and undirected network we derive lower and upper bounds on its algebraic connectivity with respect to the reference signal the bounds are derived by partitioning the network in terms of distance of each node from the pinning set upper and lower bounds for two networks with differing topologies are computed to demonstrate the tightness of the derived results it is shown using the derived bounds how requirements on the number of pinning nodes and pinning gain required for achieving stability or a specified convergence rate for the network can be easily obtained

controllability of multiplex multi time scale networks the paradigm of layered networks is used to describe many real world systems from biological networks to social organizations and transportation systems while recently there has been much progress in understanding the general properties of multilayer networks our understanding of how to control such systems remains limited one fundamental aspect that makes this endeavor challenging is that each layer can operate at a different time scale thus we cannot directly apply standard ideas from structural control theory of individual networks here we address the problem of controlling multilayer and multi time scale networks focusing on two layer multiplex networks with one to one interlayer coupling we investigate the practically relevant case when the control signal is applied to the nodes of one layer we develop a theory based on disjoint path covers to determine the minimum number of inputs n i necessary for full control we show that if both layers operate on the same time scale then the network structure of both layers equally affect controllability in the presence of time scale separation controllability is enhanced if the controller interacts with the faster layer n i decreases as the time scale difference increases up to a critical time scale difference above which n i remains constant and is completely determined by the faster layer we show that the critical time scale difference is large if layer i is easy and layer ii is hard to control in isolation in contrast control becomes increasingly difficult if the controller interacts with the layer operating on the slower time scale and increasing time scale separation leads to increased n i again up to a critical value above which n i still depends on the structure of both layers this critical value is largely determined by the longest path in the faster layer that does not involve cycles by identifying the underlying mechanisms that connect time scale difference and controllability for a simplified model we provide crucial insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity

upper and lower bounds for controllable subspaces of networks of diffusively coupled agents this technical note studies the controllability of diffusively coupled networks where some agents called leaders are under the influence of external control inputs first we consider networks where agents have general linear dynamics then we turn our attention to infer network controllability from its underlying graph topology to do this we consider networks with agents having single integrator dynamics for such networks we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions respectively we also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders

altering synchronizability by adding and deleting edges for scale free networks abstract in this paper we propose two methods for altering the synchronizability of scale free networks 1 adding edges between the max degree nodes and min degree nodes 2 deleting edges between the max degree nodes and max degree nodes after adding and deleting edges we find that the former adding process can weaken synchronizability while the latter deleting process can enhance it the two processes adding and deleting can preserve the scale free structure the study of the average clustering coefficient indicates that it is not the most closely correlated with the synchronizability among the topological features considered our work also suggests that there are some essential relations between the network synchronization and the dynamics of economic systems they can be used to deal with some problems in the real world such as relieving the economic crisis in addition the adding and deleting processes may have potential applications in modifying network structure in view of their low cost

combination of direct and indirect evidence in mixed treatment comparisons mixed treatment comparison mtc meta analysis is a generalization of standard pairwise meta analysis for a vs b trials to data structures that include for example a vs b b vs c and a vs c trials there are two roles for mtc one is to strengthen inference concerning the relative efficacy of two treatments by including both direct and indirect comparisons the other is to facilitate simultaneous inference regarding all treatments in order for example to select the best treatment in this paper we present a range of bayesian hierarchical models using the markov chain monte carlo software winbugs these are multivariate random effects models that allow for variation in true treatment effects across trials we consider models where the between trials variance is homogeneous across treatment comparisons as well as heterogeneous variance models we also compare models with fixed unconstrained baseline study effects with models with random baselines drawn from a common distribution these models are applied to an illustrative data set and posterior parameter distributions are compared we discuss model critique and model selection illustrating the role of bayesian deviance analysis and node based model criticism the assumptions underlying the mtc models and their parameterization are also discussed

numerical solution of the time fractional reaction diffusion equation with a moving boundary abstract a fractional reaction diffusion model with a moving boundary is presented in this paper an efficient numerical method is constructed to solve this moving boundary problem our method makes use of a finite difference approximation for the temporal discretization and spectral approximation for the spatial discretization the stability and convergence of the method is studied and the errors of both the semi discrete and fully discrete schemes are derived numerical examples motivated by problems from developmental biology show a good agreement with the theoretical analysis and illustrate the efficiency of our method

instability and controllability of linearly coupled oscillators eigenvalue analysis the stability and controllability of synchronous chaos of linearly coupled oscillators are investigated in detail based on eigenvalue analysis the complicated coupled problem is reduced to two independent problems clarifying the unstable regions of a modified single site system and specifying the eigenvalue distribution of the linear coupling and control matrix both problems can be easily solved local injections pinnings are suggested to synchronize chaos the dependence of the controllability on pinning density and the diffusive and gradient couplings is studied it is shown that high control efficiency can be achieved in the strong gradient coupling case for certain classes of unstable region distributions s1063 651x 98 14410 0

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

a multiscale galerkin approach for a class of nonlinear coupled reaction diffusion systems in complex media abstract a galerkin approach for a class of multiscale reaction diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented this type of models are obtained e g by upscaling of processes in chemical engineering particularly in catalysis biochemistry or geochemistry exploiting the special structure of the models the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure uniform estimates for the finite dimensional approximations are proven based on these estimates the convergence of the approximating sequence is shown this approach can be used as a basis for the numerical computation of the solution

toward synchronization in networks with nonlinear dynamics a submodular optimization framework synchronization underlies phenomena including memory and perception in the brain coordinated motion of animal flocks and stability of the power grid these synchronization phenomena are often modeled through networks of phase coupled oscillating nodes heterogeneity in the node dynamics however may prevent such networks from achieving the required level of synchronization in order to guarantee synchronization external inputs can be used to pin a subset of nodes to a reference frequency while the remaining nodes are steered toward synchronization via local coupling in this paper we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from a desired set of initial states we derive threshold based sufficient conditions for synchronization and then prove that these conditions are equivalent to constraints on monotone submodular functions over partition matroids based on this connection we map the sufficient conditions for synchronization to constraints on submodular functions leading to efficient algorithms with provable optimality bounds for selecting input nodes we illustrate our approach via numerical studies of synchronization in power systems

a proof of concept phase ii non inferiority criterion traditional phase iii non inferiority trials require compelling evidence that the treatment vs control effect bf is better than a pre specified non inferiority margin ni the standard approach compares this margin to the 95 per cent confidence interval of the effect parameter in the phase ii setting in order to declare proof of concept poc for non inferiority and proceed in the development of the drug different criteria that are specifically tailored toward company internal decision making may be more appropriate for example less evidence may be needed as long as the effect estimate is reasonably convincing we propose a non inferiority design that addresses the specifics of the phase ii setting the requirements are that 1 the effect estimate be better than a critical threshold c and 2 the type i error with regard to ni is controlled at a pre specified level this design is compared with the traditional design from a frequentist as well as a bayesian perspective where the latter relies on the level of proof lop metric i e the probability that the true effect is better than effect values of interest clinical input is required to establish the value c which makes the design transparent and improves interactions within clinical teams the proposed design is illustrated for a non inferiority trial for a time to event endpoint in oncology

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

characterization and control of small world networks recently watts and strogatz nature london 393 440 1998 offered an interesting model of small world networks here we concretize the concept of a faraway connection in a network by defining a far edge our definition is algorithmic and independent of any external parameters such as topology of the underlying space of the network we show that it is possible to control the spread of an epidemic by using the knowledge of far edges we also suggest a model for better product advertisement using the far edges our findings indicate that the number of far edges can be a good intrinsic parameter to characterize small world phenomena

on synchronized regions of discrete time complex dynamical networks in this paper the local synchronization of discrete time complex networks is studied first it is shown that for any natural number n there exists a discrete time network which has at least disconnected synchronized regions for local synchronization which implies the possibility of intermittent synchronization behaviors different from the continuous time networks the existence of an unbounded synchronized region is impossible for discrete time networks the convexity of the synchronized regions is also characterized based on the stability of a class of matrix pencils which is useful for enlarging the stability region so as to improve the network synchronizability

projective cluster synchronization in drive response dynamical networks abstract in this paper we study the projective cluster synchronization in a drive response dynamical network with 1 n coupled partially linear chaotic systems because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable pinning control ideas are adopted to direct the different scaling factors onto the desired values it is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster numerical simulations on the chaotic lorenz system are illustrated to verify the theoretical results

a mathematical model for the sulphur dioxide aggression to calcium carbonate stones numerical approximation and asymptotic analysis we introduce a degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide for this system we present some finite element and finite difference schemes to approximate its solutions numerical stability is given under suitable cfl conditions finally by means of a formal scaling the qualitative behavior of the solutions for large times is investigated and a numerical verification of this asymptotics is given our results are in qualitative agreement with the experimental behavior observed in the chemical literature

structure identification of uncertain general complex dynamical networks with time delay it is well known that many real world complex networks have various uncertain information such as unknown or uncertain topological structure and node dynamics the structure identification problem has theoretical and practical importance for uncertain complex dynamical networks at the same time time delay often appears in the state variables or coupling coefficients of various practical complex networks this paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay in particular this method is also effective for uncertain delayed complex dynamical networks with different node dynamics moreover the proposed method can be easily extended to monitor the on line evolution of network topological structure finally three representative examples are then given to verify the effectiveness of the proposed approach

quasi synchronization of heterogeneous dynamic networks via distributed impulsive control this paper studies leader follower synchronization in heterogeneous dynamic networks via distributed impulsive control the goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound referred to as quasi synchronization some fundamental and yet challenging problems are addressed 1 how to obtain a tight quasi synchronization error bound 2 how many and which nodes should be controlled 3 how to design the coupling strength to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi synchronization within a prescribed error bound first some general quasi synchronization conditions are derived with explicit expressions of the error bound second the pinning strategy and the coupling strength in achieving quasi synchronization are explored and expressed in term of impulse intervals it is interesting to find that a large coupling strength will destroy synchrony in contrast to continuous pinning control furthermore the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small a new concept referred to as impulse pinning controllability is introduced to the case that impulses cannot take place too frequently third an optimization of the error bound is discussed and formulated under a prescribed error bound the design problem of the coupling strength pinned nodes and impulse intervals is solved finally three examples are given to verify the theoretical results

key node selection in minimum cost control of complex networks abstract finding the key node set that is connected with a given number of external control sources for driving complex networks from initial state to any predefined state with minimum cost known as minimum cost control problem is critically important but remains largely open by defining an importance index for each node we propose revisited projected gradient method extension r pgme in monte carlo scenario to determine key node set it is found that the importance index of a node is strongly correlated to occurrence rate of that node to be selected as a key node in monte carlo realizations for three elementary topologies erd s renyi and scale free networks we also discover the distribution patterns of key nodes when the control cost reaches its minimum specifically the importance indices of all nodes in an elementary stem show a quasi periodic distribution with high peak values in the beginning and end of a quasi period while they approach to a uniform distribution in an elementary cycle we further point out that an elementary dilation can be regarded as two elementary stems whose lengths are the closest and the importance indices in each stem present similar distribution as in an elementary stem our results provide a better understanding and deep insight of locating the key nodes in different topologies with minimum control cost

global synchronization of complex networks perturbed by the poisson noise in this paper the problem of stochastic synchronization analysis is investigated for complex networks perturbed by the poisson noise by using the key tool such as the infinitesimal operator for stochastic differential equations driven by the poisson process this paper proposes a globally exponentially synchronization criterion in mean square for complex networks perturbed by the poisson noise finally numerical examples are provided to demonstrate the effectiveness of the proposed approach

synchronization of complex networks via aperiodically intermittent pinning control in this note synchronization for linearly coupled network is investigated by pinning a simple aperiodically intermittent controller nodes dynamical behaviors in the network are described by continuous time ordinary differential equations some sufficient conditions to guarantee global synchronization are presented furthermore an adaptive algorithm is designed for the pinning control gain and its validity is also proved rigorously finally numerical simulations are given to demonstrate the correctness of obtained results

the effect of control strength on the synchronization in pinning control questions this paper investigates the effects of control strength on nonlinearly coupled systems in the process of synchronization where the coupling strength is an invariable constant under the assumption of an asymmetric and reducible coupling matrix two comparable sufficient conditions are obtained by using the lyapunov direct method moreover a rough bound for the control strength is presented a simple simulation is also given to show the validity of the theorems this work improves the current results that we have

cluster synchronization in directed networks of non identical systems with noises via random pinning control abstract this paper is concerned with the issue of mean square cluster synchronization in directed networks which consist of non identical nodes infected by communication noises the pinning control method is employed in designing controllers for guaranteeing cluster synchronization meanwhile all the controllers are supposed to occur with different probabilities by introducing the bernoulli stochastic variables based on the lyapunov stability theory and the stochastic theory the sufficient synchronization conditions are derived and proved theoretically which are mainly for the controllers to be designed and the noise intensities finally some numerical examples are presented to demonstrate the effectiveness of the results

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

random talk random walk and synchronizability in a moving neighborhood network abstract we examine the synchronization problem for a group of dynamic agents that communicate via a moving neighborhood network each agent is modeled as a random walker in a finite lattice and is equipped with an oscillator the communication network topology changes randomly and is dictated by the agents locations in the lattice information sharing talking is possible only for geographically neighboring agents this complex system is a time varying jump nonlinear system we introduce the concept of long time expected communication network defined as the ergodic limit of a stochastic time varying network we show that if the long time expected network supports synchronization then so does the stochastic network when the agents diffuse sufficiently quickly in the lattice

impulsively control complex networks with different dynamical nodes to its trivial equilibrium this paper investigates the stability of complex networks with different dynamical nodes by impulsive control a model of complex network with different dynamical nodes is presented and then the impulsive controlled network is written as a whole vector equation specially the coupling matrix in this model is not assumed to be diffusive or irreducible some criteria and corollary are derived for the presented impulsive controlled complex networks furthermore the results are illustrated by a complex network composed of the chaotic lorenz systems and chua s circuit systems all the numerical simulations verify the correctness of the theoretical results

reconciling bayesian and frequentist evidence in the one sided testing problem abstract for the one sided hypothesis testing problem it is shown that it is possible to reconcile bayesian evidence against h 0 expressed in terms of the posterior probability that h 0 is true with frequentist evidence against h 0 expressed in terms of the p value in fact for many classes of prior distributions it is shown that the infimum of the bayesian posterior probability of h 0 is equal to the p value in other cases the infimum is less than the p value the results are in contrast to recent work of berger and sellke 1987 in the two sided point null case where it was found that the p value is much smaller than the bayesian infimum some comments on the point null problem are also given

mutual synchronization and clustering in randomly coupled chaotic dynamical networks we introduce and study systems of randomly coupled maps rcm where the relevant parameter is the degree of connectivity in the system global almost synchronized states are found equivalent to the synchronization observed in globally coupled maps until a certain critical threshold for the connectivity is reached we further show that not only the average connectivity but also the architecture of the couplings is responsible for the cluster structure observed we analyse the different phases of the system and use various correlation measures in order to detect ordered non synchronized states finally it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

stabilizing weighted complex networks real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper the v stability problem is investigated for a class of asymmetric weighted coupled networks with nonidentical node dynamics which includes the unweighted network as a special case pinning control is suggested to stabilize such a coupled network the complicated stabilization problem is reduced to measuring the semi negative property of the characteristic matrix which embodies not only the network topology but also the node self dynamics and the control gains it is found that network stabilizability depends critically on the second largest eigenvalue of the characteristic matrix the smaller the second largest eigenvalue is the more the network is pinning controllable numerical simulations of two representative networks composed of non chaotic systems and chaotic systems respectively are shown for illustration and verification

a moving boundary problem for concrete carbonation global existence and uniqueness of weak solutions this paper deals with a one dimensional coupled system of semi linear parabolic equations with a kinetic condition on the moving boundary the latter furnishes the driving force for the moving boundary the main result is a global existence and uniqueness theorem of positive weak solutions the system under consideration is modelled on the so called carbonation of concrete a prototypical chemical corrosion process in a porous solid concrete which incorporates slow diffusive transport interfacial exchange between wet and dry parts of the pores and in particular a fast reaction in thin layers here idealized as a moving boundary surface in the solid we include simulation results showing that the model captures the qualitative behaviour of the carbonation process

maximum performance at minimum cost in network synchronization we consider two optimization problems on synchronization of oscillator networks maximization of synchronizability and minimization of synchronization cost we first develop an extension of the well known master stability framework to the case of non diagonalizable laplacian matrices we then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the laplacian eigenvalues among the optimal networks we identify a subclass of hierarchical networks characterized by the absence of feedback loops and the normalization of inputs we show that most optimal networks are directed and non diagonalizable necessitating the extension of the framework we also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role

chaos synchronization of general complex dynamical networks recently it has been demonstrated that many large scale complex dynamical networks display a collective synchronization motion here we introduce a time varying complex dynamical network model and further investigate its synchronization phenomenon based on this new complex network model two network chaos synchronization theorems are proved we show that the chaos synchronization of a time varying complex network is determined by means of the inner coupled link matrix the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network especially we do not assume that the coupled configuration matrix is symmetric and its off diagonal elements are nonnegative which in a way generalizes the related results existing in the literature

consensus controllability observability and robust design for leader following linear multi agent systems a b s t r a c t this paper considers for leader following linear multi agent systems mas connected by switching graphs the consensus controllability and observability and extends the existing results which are valid only for fixed graph case unlike the general controllability and observability problems which require each state to be controllable and observable we only examine the consensus state to be controllable and the tracking error states between the followers and the leader to be observable as for the consensus controllability the admissible control input for each follower agent can only obtain relative and local information from its neighbors and the control objective is to render the mas to achieve consensus in the sense of convergence of each follower s state to that of a leader agent as for the consensus observability the output of the mas is the information flow in the multi agent network and the observation task is to reconstruct the tracking error states between the followers and the leader it is demonstrated in this paper that the controllability and observability of each individual system and the jointly connected switching topology including fixed topology as a special case jointly imply the consensus controllability and observability of the mas the consensus controllability property is used in the robust leader following consensus problem and the consensus observability property is used in the robust observer based leader following consensus problem both under switching topology

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

synchronization is optimal in nondiagonalizable networks we consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology by extending the master stability formalism to all possible network structures we show that unless some oscillator is linked to all the others maximally synchronizable networks are necessarily nondiagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths the results provide insights into hierarchical structures observed in complex networks in which synchronization is important

pinning control of weighted general complex dynamical networks with time delay abstract time delays commonly exist in the real world in the present work we consider weighted general complex dynamical networks with time delay which are undirected and connected control of such networks by applying local feedback injections to a fraction of network nodes is investigated for both continuous time and discrete time cases both delay independent and delay dependent asymptotical stability criteria for network stabilization are derived it is also shown that the whole network can be stabilized by controlling only one node the efficiency of the derived results was illustrated by numerical examples

asymptotics of reaction diffusion fronts with one static and one diffusing reactant abstract the long time behavior of a reaction diffusion front between one static e g porous solid reactant a and one initially separated diffusing reactant b is analyzed for the mean field reaction rate density r a b k a m b n a uniformly valid asymptotic approximation is constructed from matched self similar solutions in a reaction front of width w t where r t enters the dominant balance and a diffusion layer of width w t 1 2 where r is negligible the limiting solution exists if and only if m n 1 in which case the scaling exponents are uniquely given by m 1 2 m 1 and m m 1 in the diffusion layer the common ad hoc approximation of neglecting reactions is given mathematical justification and the exact transient decay of the reaction rate is derived the physical effects of higher order kinetics m n 1 such as the broadening of the reaction front and the slowing of transients are also discussed

weak solutions of coupled dual porosity flows in fractured rock mass and structured porous media abstract this paper deals with a fully nonlinear degenerate parabolic system with natural critical growths and under non linear boundary conditions such problems arise from the heat and water flow through a partially saturated fractured rock mass and structured porous media existence of a global weak solution of the problem on an arbitrary interval of time is proved by means of semidiscretization in time deriving suitable a priori estimates based on w 1 p regularity of the approximate solution and by passing to the limit from discrete approximations

cluster synchronization in star like complex networks the cluster synchronization of a star like complex network which consists of n nodes coupled with a common environment is discussed by using the matrix theory and the lyapunov function approach a sufficient condition about the existence and asymptotic stability of a cluster synchronization invariant manifold is derived the effectiveness of the sufficient condition is illustrated by two examples in addition the two examples also show that in the star like complex network in which the individual node is chaotic or non chaotic the dynamics of some nodes in the cluster synchronization invariant manifold can be non chaotic or chaotic

enforcing social behavior in an ising model with complex neighborhoods abstract we consider the problem of enforcing desired behavior in a population of individuals modeled by an ising model although there is a large literature dealing with social interaction models the problem of controlling behavior in a system modeled by the ising model seems to be an unexplored field first we provide and analytically characterize an optimal policy that may be used to achieve this objective second we show that complex neighborhoods highly influence the decision making process third we use lagrange multipliers associated to some constraints of a related problem to identify the role of individuals in the system

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

controllability of complex networks via pinning we study the problem of controlling a general complex network toward an assigned synchronous evolution by means of a pinning control strategy we define the pinning controllability of the network in terms of the spectral properties of an extended network topology the roles of the control and coupling gains as well as of the number of pinned nodes are also discussed

adaptive synchronization between two different noise perturbed chaotic systems with fully unknown parameters abstract this paper investigates adaptive synchronization between two different noise perturbed chaotic systems with fully unknown parameters based on lyapunov stability theory the general expression of the suitable nonlinear adaptive synchronization controller is developed at the same time the noise perturbed update laws of parameters are proposed to guarantee the synchronization of two different unknown chaotic systems theoretical analysis and numerical simulations on adaptive synchronization between rossler system and noise perturbed chua s circuits lorenz system and noise perturbed chen system with fully unknown parameters show the efficiency of the proposed adaptive scheme

experiments on node to node pinning control of chua s circuits abstract in this paper we study the global intermittent pinning controllability of networks of coupled chaotic oscillators we explore the feasibility of the recently presented node to node pinning control strategy through experiments on chua s circuits we focus on the case of two peer to peer coupled chua s circuits and we build a novel test bed platform comprised of three inductorless chua s oscillators we investigate the effect of a variety of design parameters on synchronization performance including the coupling strength between the oscillators the control gains and the switching frequency of node to node pinning control experimental results demonstrate the effectiveness of this novel pinning control strategy in rapidly taming chaotic oscillator dynamics onto desired reference trajectories while minimizing the overall control effort and the number of pinned network sites from an analytical standpoint we present sufficient conditions for global node to node pinning controllability and we estimate the maximum switching period for network controllability by adapting and integrating available results on lyapunov stability theory and partial averaging techniques

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

effects of degree correlation on the controllability of networks abstract in this paper we investigate the effects of degree correlation on the controllability of undirected networks with different degree mixing patterns based on simulation analysis considering random pinning max degree pinning and mix degree pinning some relevance factors on controllability such as the control gain and the number of pinned nodes are discussed in detail it is found that disassortative mixing enhances the network controllability contrast to assortative mixing to which the network controllability is sensible furthermore too large or too low value of the feedback gain can reduce the controllability from the viewpoint of practical application mix degree pinning strategy is suggested in assortative network while in disassortative network max degree pinning scheme is better than random pinning

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

criteria for global pinning controllability of complex networks in this paper we study pinning controllability of networks of coupled dynamical systems in particular we study the problem of asymptotically driving a network of coupled identical oscillators onto some desired common reference trajectory by actively controlling only a limited subset of the whole network the reference trajectory is generated by an exogenous independent oscillator and pinned nodes are coupled to it through a linear state feedback we describe the time evolution of the complex dynamical system in terms of the error dynamics thereby we reformulate the pinning controllability problem as a global asymptotic stability problem by using lyapunov stability theory and algebraic graph theory we establish tractable sufficient conditions for global pinning controllability in terms of the network topology the oscillator dynamics and the linear state feedback

choosing effective controlled nodes for scale free network synchronization abstract previous studies concerning pinning control of complex network synchronization have very often demonstrated that in an unweighted symmetrical scale free network controlling the high degree nodes is more efficient than controlling randomly chosen ones due to the heterogeneity of the node degree or edge connection distribution of the scale free network small degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network this raises the question of whether or not controlling the high degree nodes is always better than controlling the small ones in scale free networks our answer to this is yes and no in this study we carry out extensive numerical simulations to show that in an unweighted symmetrical barabasi albert scale free network when the portion of controlled nodes is relatively large controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones however we also show that for normalized weighted scale free networks controlling the big nodes is in fact always better than controlling the small ones

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

phase synchronization in small world networks of chaotic oscillators abstract small world networks are highly clustered networks with small average distance among the vertices there are many natural and technological networks that present this kind of connections we study the phase synchronization of small world chaotic oscillator networks in this paper we find that for rossler oscillator networks in the synchronous regime the oscillation phases are locked while the amplitudes vary chaotically we further show the dependence of phase synchronization on the network coupling strength the product of the shortcuts adding probability and the number of chaotic oscillators as well as the maximal frequency mismatch

finding and evaluating the hierarchical structure in complex networks a number of recent studies have focused on a statistical property of networked systems the hierarchical structure the problem of detecting and characterizing the hierarchical structure has recently attracted considerable attention in this paper it is rewritten as optimization in terms of the eigenvalues and eigenvectors based on that an algorithm for reconstructing the hierarchical structure of complex networks is proposed it is tested on some real world graphs and is found to offer high sensitivity and reliability

analysis of pinning controlled networks a renormalization approach in this paper a renormalization approach is introduced for analyzing pinning controlled networks the renormalization process consists of two operations edge weighting and node reduction and is built on a new concept of passivity comparison in the sense of lyapunov v stability furthermore a cascaded model resulted from the renormalization process in a layer structure is presented for estimating the v stability of a network finally simulation studies are presented for illustration and verification of the theoretical results

a class of uncontrollable diffusively coupled multiagent systems with multichain topologies we construct systematically a class of uncontrollable diffusively coupled multiagent systems with a single leader and multichain topologies for studying the controllability of diffusively coupled multiagent systems such identified uncontrollable systems serve as counterexamples that prove the need to modify the existing sufficient condition using graph partitioning characterization the uncontrollability of the constructed multichain structures can be preserved when the structures are further augmented to get better connected the paper also provides an algorithm to obtain the minimal leader invariant relaxed equitable partition for the graph associated with any diffusively coupled multiagent system guided by a single leader

robust adaptive synchronization of a class of chaotic systems via fuzzy bilinear observer using projection operator this study focuses on the problem of robust adaptive synchronization of uncertain bilinear chaotic systems a takagisugeno fuzzy bilinear system tsfbs is employed herein to describe a bilinear chaotic system a robust adaptive observer which estimates the states of the tsfbs is also developed advanced adaptive laws using a projection operator are designed to achieve both the robustness for the external disturbances and the adaptation of unknown system parameters a comparison with the existing observer shows that the proposed observer can achieve a faster parameter adaptation and a robust synchronization for an uncertain tsfbs with disturbances when the adaptive laws are utilized the asymptotic stability and the robust performance of the error dynamics are guaranteed by some assumptions and the lyapunov stability theory we verify the effectiveness of the proposed scheme using examples of the generalized lorenz system in various aspects

measure the structure similarity of nodes in complex networks based on relative entropy abstract similarity of nodes is a basic structure quantification in complex networks lots of methods in research on complex networks are based on nodes similarity such as node s classification network s community structure detection network s link prediction and so on therefore how to measure nodes similarity is an important problem in complex networks in this paper a new method is proposed to measure nodes structure similarity based on relative entropy and each node s local structure in the new method each node s structure feature can be quantified as a special kind of information the quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information then relative entropy is used to measure the difference between each pair of nodes structural information at last the value of relative entropy between each pair of nodes is used to measure nodes structure similarity in complex networks comparing with existing methods the new method is more accuracy to measure nodes structure similarity

stochastic synchronization in blinking networks of chaotic maps in this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on off couplings between any pair of nodes we focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold by projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics we establish a necessary and sufficient condition for stochastic synchronization based on the largest lyapunov exponent of the map and the spectral radius of such matrix this condition is further simplified by computing closed form results for the spectral properties of the moments of the graph laplacian associated to the intermittent coupling and using classical eigenvalue bounds we illustrate the main results through simulations on synchronization of chaotic henon maps

convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media in this paper we discuss the numerical analysis of an upscaled core scale model describing the transport precipitation and dissolution of solutes in a porous medium the particularity lies in the modeling of the reaction term especially the dissolution term which has a multivalued character we consider the weak formulation for the upscaled equation and provide rigorous stability and convergence results for both the semi discrete time discretization and the fully discrete schemes in doing so compactness arguments are employed