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

new maximal functions and multiple weights for the multilinear calderon zygmund theory a multi sub linear maximal operator that acts on the product of m lebesgue spaces and is smaller than the m fold product of the hardy littlewood maximal function is studied the operator is used to obtain a precise control on multilinear singular integral operators of calderon zygmund type and to build a theory of weights adapted to the multilinear setting a natural variant of the operator which is useful to control certain commutators of multilinear calderon zygmund operators with bmo functions is then considered the optimal range of strong type estimates a sharp end point estimate and weighted norm inequalities involving both the classical muckenhoupt weights and the new multilinear ones are also obtained for the commutators

design of networked control systems with packet dropouts this note is concerned with stability and controller design of networked control systems ncss with packet dropouts new ncs models are provided considering both single and multiple packet transmissions both sensor to controller s c and controller to actuator c a packet dropouts are modeled and their history behavior is described by different independent markov chains in term of the given models sufficient conditions for stochastic stability are derived in the form of linear matrix inequalities lmis and corresponding control laws are given numerical examples illustrate the effectiveness of the results

optimal estimation and control for lossy network stability convergence and performance in this paper we study the problems of optimal estimation and control i e the linear quadratic gaussian lqg control for systems with packet losses but without acknowledgment such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses for such system which is usually called as a user datagram protocol udp like system the optimal estimation is nonlinear and its calculation is time consuming making its corresponding optimal lqg problem complicated we first propose two conditions 1 the sensor has some computation abilities and 2 the control command exerted to the plant is known to the sensor for a udp like system satisfying these two conditions we derive the optimal estimation by constructing the finite and infinite product probability measure spaces for the estimation error covariances eec we give the stability condition for the expected eec and show the existence of a measurable function to which the eec converges in distribution and propose some practical methods to evaluate the estimation performance finally the lqg controllers are derived and the conditions for the mean square stability of the closed loop system are established

subgraph centrality in complex networks we introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network smaller subgraphs are given more weight than larger ones which makes this measure appropriate for characterizing network motifs we show that the subgraph centrality c s i can be obtained mathematically from the spectra of the adjacency matrix of the network this measure is better able to discriminate the nodes of a network than alternate measures such as degree closeness betweenness and eigenvector centralities we study eight real world networks for which c s i displays useful and desirable properties such as clear ranking of nodes and scale free characteristics compared with the number of links per node the ranking introduced by c s i for the nodes in the protein interaction network of s cereviciae is more highly correlated with the lethality of individual proteins removed from the proteome

brief paper l2 norm performance index of synchronization and lqr control synthesis of complex networks in this paper the synchronizability problem of dynamical networks is addressed where better synchronizability means faster network synchronization with lower vibration the l 2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability for the equilibrium synchronization case it is shown that there is a close relationship between the l 2 norm of the error vector e and the h 2 norm of the transfer function g of the linearized network about the equilibrium point consequently the effect of the network coupling topology on the h 2 norm of the transfer function g is analyzed finally an lqr controller is designed according to the lqr problem in modern control theory which can drive the whole network to its equilibrium point and meanwhile minimize the l 2 norm of the output of the linearized network

collective phase description of coupled oscillators with general network structure we develop a collective phase description for a population of nonidentical limit cycle oscillators with any network structure undergoing fully phase locked collective oscillations the whole network dynamics can be described by a single collective phase variable we derive a general formula for the collective phase sensitivity which quantifies the phase response of the whole network to weak external perturbations applied to the constituent oscillators moreover we consider weakly interacting multiple networks and develop an effective phase coupling description for them several examples are given to illustrate our theory

brief stochastic optimal control and analysis of stability of networked control systems with long delay in this paper stochastic optimal controllers of networked control systems whose network induced delay is longer than a sampling period are designed for the two cases of the system with either full state information or partial state information the controllers are shown to render corresponding networked control systems exponentially mean square stable the optimal estimator of the system state is presented when the system has partial state information and network induced delay is longer than a sampling period the separation theorem is proved to still hold in such networked control systems

policy iteration adaptive dynamic programming algorithm for discrete time nonlinear systems this paper is concerned with a new discrete time policy iteration adaptive dynamic programming adp method for solving the infinite horizon optimal control problem of nonlinear systems the idea is to use an iterative adp technique to obtain the iterative control law which optimizes the iterative performance index function the main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete time nonlinear systems for the first time it shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the hamilton jacobi bellman equation it is also proven that any of the iterative control laws can stabilize the nonlinear systems neural networks are used to approximate the performance index function and compute the optimal control law respectively for facilitating the implementation of the iterative adp algorithm where the convergence of the weight matrices is analyzed finally the numerical results and analysis are presented to illustrate the performance of the developed method

enhancing synchronizability of diffusively coupled dynamical networks a survey in this paper we review the literature on enhancing synchronizability of diffusively coupled dynamical networks with identical nodes the last decade has witnessed intensive investigations on the collective behavior over complex networks and synchronization of dynamical systems is the most common form of collective behavior for many applications it is desired that the synchronizability the ability of networks in synchronizing activity of their individual dynamical units is enhanced there are a number of methods for improving the synchronization properties of dynamical networks through structural perturbation in this paper we survey such methods including adding removing nodes and or edges rewiring the links and graph weighting these methods often try to enhance the synchronizability through minimizing the eigenratio of the laplacian matrix of the connection graph a synchronizability measure based on the master stability function formalism we also assess the performance of the methods by numerical simulations on a number of real world networks as well as those generated through models such as preferential attachment watts strogatz and erdos renyi

synchronization in complex dynamical networks with nonsymmetric coupling based on the work of nishikawa and motter who have extended the well known master stability framework to include non diagonalizable cases we develop another extension of the master stability framework to obtain criteria for global synchronization several criteria for global synchronization are provided which generalize some previous results the jordan canonical transformation method is used in stead of the matrix diagonalization method especially we show clearly that the synchronizability of a dynamical network with nonsymmetric coupling is not always characterized by its second largest eigenvalue even though all the eigenvalues of the nonsymmetric coupling matrix are real furthermore the effects of the asymmetry of coupling on synchronizability of networks with different structures are analyzed numerical simulations are also done to illustrate and verify the theoretical results on networks in which each node is a dynamical limit cycle oscillator consisting of a two cell cellular neural network

a multilinear schur test and multiplier operators abstract a multilinear version of schur s test is obtained for products of l p spaces and is used to derive boundedness for multilinear multiplier operators acting on sobolev and besov spaces

the number and degree distribution of spanning trees in the tower of hanoi graph the number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph such as its reliability communication aspects synchronization and so on however the practical enumeration of spanning trees and the study of their properties remain a challenge particularly for large networks in this paper we study the number and degree distribution of the spanning trees in the hanoi graph we first establish recursion relations between the number of spanning trees and other spanning subgraphs of the hanoi graph from which we find an exact analytical expression for the number of spanning trees of the n disc hanoi graph this result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree then we introduce a vertex labeling which allows to find for each vertex of the graph its degree distribution among all possible spanning trees

boundedness of operators of hardy type in λ p q spaces and weighted mixed inequalities for singular integral operators we consider certain n dimensional operators of hardy type and we study their boundedness in these spaces were introduced by m j carro and j soria and include weighted l p q spaces and classical lorentz spaces as an application we obtain mixed weak type inequalities for calderon zygmund singular integrals improving results due to k andersen and b muckenhoupt

predicting the synchronization time in coupled map networks an analytical expression for the synchronization time in coupled map networks is given by means of the expression the synchronization time for any given network can be predicted accurately furthermore for networks in which the distributions of nontrivial eigenvalues of coupling matrices have some unique characteristics analytical results for the minimal synchronization time are given

mean field approximation of two coupled populations of excitable units the analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of n stochastic excitable units each is performed by studying an approximate system obtained by replacing each population with the corresponding mean field model in the exact system one has the units within an ensemble communicating via the time delayed linear couplings whereas the interensemble terms involve the nonlinear time delayed interaction mediated by the appropriate global variables the aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system governed by a set of 4n stochastic delay differential equations for the microscopic dynamics can accurately be reproduced by a flow containing just four deterministic delay differential equations which describe the evolution of the mean field based variables in particular the considered issues include determining the parameter domains where the stationary state is stable the scenarios for the onset and the time delay induced suppression of the collective mode as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state we show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations like those with symmetrical or asymmetrical interpopulation couplings

approximate optimal control of affine nonlinear continuous time systems using event sampled neurodynamic programming this paper presents an approximate optimal control of nonlinear continuous time systems in affine form by using the adaptive dynamic programming adp with event sampled state and input vectors the knowledge of the system dynamics is relaxed by using a neural network nn identifier with event sampled inputs the value function which becomes an approximate solution to the hamilton jacobi bellman equation is generated by using event sampled nn approximator subsequently the nn identifier and the approximated value function are utilized to obtain the optimal control policy both the identifier and value function approximator weights are tuned only at the event sampled instants leading to an aperiodic update scheme a novel adaptive event sampling condition is designed to determine the sampling instants such that the approximation accuracy and the stability are maintained a positive lower bound on the minimum inter sample time is guaranteed to avoid accumulation point and the dependence of inter sample time upon the nn weight estimates is analyzed a local ultimate boundedness of the resulting nonlinear impulsive dynamical closed loop system is shown finally a numerical example is utilized to evaluate the performance of the near optimal design the net result is the design of an event sampled adp based controller for nonlinear continuous time systems

computational adaptive optimal control for continuous time linear systems with completely unknown dynamics this paper presents a novel policy iteration approach for finding online adaptive optimal controllers for continuous time linear systems with completely unknown system dynamics the proposed approach employs the approximate adaptive dynamic programming technique to iteratively solve the algebraic riccati equation using the online information of state and input without requiring the a priori knowledge of the system matrices in addition all iterations can be conducted by using repeatedly the same state and input information on some fixed time intervals a practical online algorithm is developed in this paper and is applied to the controller design for a turbocharged diesel engine with exhaust gas recirculation finally several aspects of future work are discussed

onset of synchronization in large networks of coupled oscillators we study the transition from incoherence to coherence in large networks of coupled phase oscillators we present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength we find that under appropriate conditions the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix we show how with an additional assumption a mean field approximation recently proposed is recovered from our results we test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied we find that our theory describes the transition well in situations in which the mean field approximation fails we study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase

synchronization limit of weakly forced nonlinear oscillators nonlinear oscillators exhibit synchronization injection locking to external periodic forcings which underlies the mutual synchronization in networks of nonlinear oscillators despite its history of synchronization and the practical importance of injection locking to date there are many important open problems of an efficient injection locking for a given oscillator in this work i elucidate a hidden mechanism governing the synchronization limit under weak forcings which is related to a widely known inequality holder s inequality this mechanism enables us to understand how and why the efficient injectionlocking is realized a general theory of synchronization limit is constructed where the maximization of the synchronization range or the stability of synchronization for general forcings including pulse trains and a fundamental limit of general m n phase locking are clarified systematically these synchronization limits and their utility are systematically verified in the hodgkin huxley neuron model as an example s online supplementary data available from stacks iop org jpa 47 402002 mmedia

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

the number of spanning trees of an infinite family of outerplanar small world and self similar graphs abstract in this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar small world and self similar graphs this number is an important graph invariant related to different topological and dynamic properties of the graph such as its reliability synchronization capability and diffusion properties the calculation of the number of spanning trees is a demanding and difficult task in particular for large graphs and thus there is much interest in obtaining closed expressions for relevant infinite graph families we have also calculated the spanning tree entropy of the graphs which we have compared with those for graphs with the same average degree

enumeration of spanning trees in planar unclustered networks abstract among a variety of subgraphs spanning trees are one of the most important and fundamental categories they are relevant to diverse aspects of networks including reliability transport self organized criticality loop erased random walks and so on in this paper we introduce a family of modular self similar planar networks with zero clustering relevant properties of this family are comparable to those networks associated with technological systems having low clustering like power grids some electronic circuits the internet and some biological systems so it is very significant to research on spanning trees of planar networks however for a large network evaluating the relevant determinant is intractable in this paper we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network using the algorithm we derive analytically the exact numbers of spanning trees in planar networks our result shows that the computational complexity is o t which is better than that of the matrix tree theorem with o m 2 t 2 where t is the number of steps and m is the girth of the planar network we also obtain the entropy for the spanning trees of a given planar network we find that the entropy of spanning trees in the studied network is small which is in sharp contrast to the previous result for planar networks with the same average degree we also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm as another application of the algorithm we give a formula for the number of spanning trees in an outerplanar network with small world features

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

on rayleigh ritz ratios of a generalized laplacian matrix of directed graphs abstract in c w wu algebraic connectivity of directed graphs linear and multilinear algebra in press a generalization of fiedler s notion of algebraic connectivity to directed graphs was presented that inherits many properties of the algebraic connectivity of undirected graphs and has applications to the synchronization of coupled dynamical systems with both constant and time varying coupling however it did not inherit nonnegativity and some of its bounds for combinatorial properties such as maximum directed cut and isoperimetric number are less strict that their undirected counterparts in particular these bounds do not have the corresponding bounds for undirected graphs as limiting cases the purpose of this paper is to present a refinement of this algebraic connectivity which preserve nonnegativity for strongly connected graphs and have bounds which contain the undirected graphs as special cases in particular we study quantities related to a generalized laplacian matrix of directed graphs and obtain bounds on combinatorial properties such as diameter bandwidth and bisection width for general directed graphs finally we give an application to the synchronization of coupled dynamical systems with constant coupling in particular we show that strong enough cooperative coupling will synchronize a network of coupled systems if the underlying directed graph is strongly connected

phase reduction theory for hybrid nonlinear oscillators hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena however the phase reduction theory a fundamental framework for analyzing the synchronization of limit cycle oscillations in rhythmic systems has mostly been restricted to smooth dynamical systems here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis control and optimization of nonlinear oscillators whose smooth models are unavailable or intractable on the basis of the generalized theory we analyze injection locking of hybrid limit cycle oscillators by periodic forcing and reveal their characteristic synchronization properties such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition we also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion

counting spanning trees of a type of generalized farey graphs abstract the farey graph f n is derived from the famous farey sequence and it is a small world network with a connectivity distribution decaying exponentially by using the matrix tree theorem zhang et al 2012 obtained the exact formula of the number of spanning trees of f n in this paper by using the electrical network method we consider a type of generalized farey graphs and give the exact solution for the number of spanning trees of these generalized farey graphs which generalizes some previous results about the farey graphs

a class of vertex edge growth small world network models having scale free self similar and hierarchical characters abstract the problem of uncovering the internal operating function of network models is intriguing demanded and attractive in researches of complex networks notice that in the past two decades a great number of artificial models are built to try to answer the above mentioned task based on the different growth ways these previous models can be divided into two categories one type possessing the preferential attachment follows a power law p k k 2 3 the other has exponential scaling feature p k k however there are no models containing above two kinds of growth ways to be presented even the study of interconnection between these two growth manners in the same model is lacking hence in this paper we construct a class of planar and self similar graphs motivated from a new attachment way vertex edge growth network operation more precisely the couple of both them we report that this model is sparse small world and hierarchical and then not only is scale free feature in our model but also lies the degree parameter 3 242 out the typical range note that we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power law parameter and the preferential attachment plays a dominate role on the development of networks over time at the end of this paper we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements

clustering and the synchronization of oscillator networks by manipulating the clustering coefficient of a network without changing its degree distribution we examine the effect of clustering on the synchronization of phase oscillators on networks with poisson and scale free degree distributions for both types of networks increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies surprisingly in scale free networks clustering promotes the synchronization of the most connected nodes hubs even though it inhibits global synchronization as a result they show an additional advanced transition instead of a single synchronization threshold this cluster enhanced synchronization of hubs may be relevant to the brain that is scale free and highly clustered

on the phase reduction and response dynamics of neural oscillator populations weundertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli recalling and extending results from the literature we compute phase response curves prcs valid near bifurcations to periodic firing for hindmarsh rose hodgkin huxley fitzhugh nagumo and morris lecar models encompassing the four generic codimension one bifurcations phase density equations are then used to analyze the role of the bifurcation and the resulting prc in responses to stimuli in particular we explore the interplay among stimulus duration baseline firing frequency and population level response patterns we interpret the results in terms of the signal processing measure of gain and discuss further applications and experimentally testable predictions

neural network based near optimal control for a class of discrete time affine nonlinear systems with control constraints in this paper the near optimal control problem for a class of nonlinear discrete time systems with control constraints is solved by iterative adaptive dynamic programming algorithm first a novel nonquadratic performance functional is introduced to overcome the control constraints and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis in the present control scheme there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme

persistence of excitation in linear systems abstract this paper develops output reachability characterizations of linear finite dimensional multivariate systems so as to translate excitation properties of system inputs to excitation properties of system outputs states or associated regression vectors such properties are of fundamental concern for convergence of algorithms involving on line identification adaptive state estimation prediction and control persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties

spectra of sparse regular graphs with loops we derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary lengths the implications of our results for the structural and dynamical properties of network models are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization analytical formulas for the spectrum are obtained for specific lengths of the loops

enumeration of spanning trees on contact graphs of disk packings abstract obtaining the number of spanning trees of complex networks is an outstanding challenge since traditional approaches such as calculating the eigenvalues of the matrix and decomposing of spanning subgraphs are awkward or even infeasible for a large scale network the foundation and importance of this quantity relating to some topological and dynamic properties prompt us to explore the role of determinant identities for laplace matrices we introduce the basic electrically equivalent technique to determine an exact analytical expression for the quantity on the contact graph of disk packings which is proposed by zhang et al 2009 our theoretical results shed light on the relationship between the microscopic change of the quantity and topological iteration of the network in particular we compare the entropy of spanning trees on the network with the other two dimensional and three dimensional lattices we show that the new model is a small world scale free network with the maximum entropy so far found in addition our method for employing the electrically equivalent technique to enumerate spanning trees is general and can be easily extended to other complex networks

positive multilinear operators acting on weighted lp spaces for j 1 2 n 1 let xj j j be finite measure spaces and let p xj denote the class of nonnegative measurable functions on xj given a positive multilinear operator m p x1 p x2 p xn p xn 1 and fixed indices p1 p2 pn q 1 we consider the problem of determining those nonnegative weight functions w1 w2 wn and v on x1 x2 xn and xn 1 respectively for which xn 1 m f1 f2 fn v q d n 11q c j 1n xj fjwj p d j1pj with c 0 independent of fj p xj j 1 2 n

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

determining individual phase response curves from aggregate population data phase reduction is an invaluable technique for investigating the dynamics of nonlinear limit cycle oscillators central to the implementation of phase reduction is the ability to calculate phase response curves prcs which describe an oscillator s response to an external perturbation current experimental techniques for inferring prcs require data from individual oscillators which can be impractical to obtain when the oscillator is part of a much larger population here we present a simple methodology to calculate prcs of individual oscillators using an aggregate signal from a large homogeneous population this methodology is shown to be accurate in the presence of interoscillator coupling and noise and can also provide a good estimate of an average prc of a heterogeneous population we also find that standard experimental techniques for prc measurement can produce misleading results when applied to aggregate population data

tracing the evolution of physics on the backbone of citation networks many innovations are inspired by past ideas in a nontrivial way tracing these origins and identifying scientific branches is crucial for research inspirations in this paper we use citation relations to identify the descendant chart i e the family tree of research papers unlike other spanning trees that focus on cost or distance minimization we make use of the nature of citations and identify the most important parent for each publication leading to a treelike backbone of the citation network measures are introduced to validate the backbone as the descendant chart we show that citation backbones can well characterize the hierarchical and fractal structure of scientific development and lead to an accurate classification of fields and subfields

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

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

synchronization analysis of delayed complex networks with time varying couplings abstract in this paper a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays the coupling configurations are not restricted to the symmetric and irreducible connections or the non negative off diagonal links the stability criteria are obtained by using lyapunov krasovskii functional method and subspace projection method these criteria reveal the relationship between coupling matrices and stability of the dynamical networks

strong effects of network architecture in the entrainment of coupled oscillator systems random networks of coupled phase oscillators representing an approximation for systems of coupled limit cycle oscillators are considered entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated for a large class of interaction functions we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization however the entrainment is significantly facilitated if the networks are directionally biased i e closer to the feedforward networks furthermore we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes the neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results

on hold or drop out of order packets in networked control systems holding or dropping out of order packets in the communications are two typical signal choosing schemes in networked control systems however neither of the two schemes can be claimed always superior to the other to improve the control performance a smart signal choosing scheme is proposed to determine whether to use the out of order packets it is theoretically proved that improved performance can be obtained based on the proposed smart signal choosing scheme two numerical examples are given to demonstrate the effectiveness of the proposed approach

on local synchronisability of nonlinear networked systems with a unit inner coupling matrix and switching topology the local synchronisation of the nonlinear networked systems with switching topology is studied in this article for the special case in which the inner coupling matrix is a unit matrix the critical idea is to convert synchronisation problem to consensus problem such that the switching topology can be dealt with effectively without any extra assumption on the relationship among the involved topologies a novel local synchronous criterion consisting of the maximum lyapunov exponent of nodal self dynamics and the consensus convergent rate of the switching topology is given to illustrate the effectiveness of the analytical results two numerical examples on chaos synchronisation are simulated respectively for the periodic switching case and randomly switching case

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

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

optimization of synchronization in gradient clustered networks we consider complex clustered networks with a gradient structure where the sizes of the clusters are distributed unevenly such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters a remarkable finding is that if the gradient field is sufficiently strong synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters these results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled oscillator networks

analysis of relative influence of nodes in directed networks many complex networks are described by directed links in such networks a link represents for example the control of one node over the other node or unidirectional information flows some centrality measures are used to determine the relative importance of nodes specifically in directed networks we analyze such a centrality measure called the influence the influence represents the importance of nodes in various dynamics such as synchronization evolutionary dynamics random walk and social dynamics we analytically calculate the influence in various networks including directed multipartite networks and a directed version of the watts strogatz small world network the global properties of networks such as hierarchy and position of shortcuts rather than local properties of the nodes such as the degree are shown to be the chief determinants of the influence of nodes in many cases the developed method is also applicable to the calculation of the pagerank we also numerically show that in a coupled oscillator system the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes for a type of random network the analytically derived threshold is approximately equal to the inverse of the influence we numerically show that this relationship also holds true in a random scale free network and a neural network

synchronization of two interacting populations of oscillators we analyze synchronization between two interacting populations of different phase oscillators for the important case of asymmetric coupling functions we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators it includes three types of bistabilities higher order entrainment and the existence of states with unusual stability properties all possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically the impact of these findings for neuroscience is discussed

weighted bilinear hardy inequalities abstract we characterize the weights w w 1 w 2 such that the weighted bilinear hardy inequality a b a x f q a x g q w x d x 1 q c a b f p 1 w 1 1 p 1 a b g p 2 w 2 1 p 2 holds for all nonnegative functions f and g with a positive constant c independent of f and g for all possible values of q p 1 and p 2 with 1 q p 1 p 2 we also characterize the good weights for the weighted bilinear n dimensional hardy inequality to hold

detecting link failures in complex network processes using remote monitoring abstract we study whether local structural changes in a complex network can be distinguished from passive remote time course measurements of the network s dynamics specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered by phrasing the detection task as a maximum a posteriori probability hypothesis testing problem we are able to obtain conditions under which the detection is 1 improved over the a priori and 2 asymptotically perfect in terms of the network spectrum and graph we find that in the case where the detector has knowledge of the network s state perfect detection is possible under general connectivity conditions regardless of the measurement location when the detector does not have state knowledge a remote signature permits improved but not perfect detection under the same connectivity conditions at its essence detectability is achieved because of the close connection between a network s topology its eigenvalues and local response characteristics

abnormal synchronizing path of delay coupled chaotic oscillators on the edge of stability abstract in this paper the transition of synchronizing path of delay coupled chaotic oscillators in a scale free network is highlighted mainly through the critical transmission delay makes chaotic oscillators be coupled on the edge of stability we find that the transition of synchronizing path is abnormal which is characterized by the following evidences a synchronization process starts with low degree rather than high degree ones b the high degree nodes do not undertake the role of hub c the synchronized subnetworks show a poor small world property as a result of hubs absence d the clustering synchronization behavior emerges even community structure is absent in the scale free network this abnormal synchronizing path suggests that the diverse synchronization behaviors occur in the same topology which implies that the relationship between dynamics and structure of network is much more complicated than the common sense that the structure is the foundation of dynamics moreover it also reveals the potential connection from the transition of synchronization behavior to disorder in real complex networks e g alzheimer disease

optimal entrainment with smooth pulse and square signals in weakly forced nonlinear oscillators abstract a physical limit of entrainability of nonlinear oscillators is considered for an external weak signal forcing this limit of entrainability is characterized by the optimization problem maximizing the width of the arnold tongue the frequency locking range versus forcing magnitude under certain practical constraints here we show a solution to this optimization problem thanks to a direct link to holder s inequality this solution defines an ideal forcing realizing the entrainment limit and as the result a fundamental limit of entrainment is clarified as follows for 1 1 entrainment we obtain i a construction of the global optimal forcing and a condition for its uniqueness in l p space with p 1 and ii a construction of the global optimal pulse like forcings in l 1 space and for m n entrainment m n some informations about the non existence of the ideal forcing iii in addition we establish definite algorithms for obtaining the global optimal forcings for 1 p and these pulse like forcings for p 1 these theoretical findings are verified by systematic extensive numerical calculations and simulations

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

perturbation analysis of complete synchronization in networks of phase oscillators the behavior of weakly coupled self sustained oscillators can often be well described by phase equations here we use the paradigm of kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections to the frequency of the fully synchronized state for nonidentical oscillators the topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network laplacian which influence the synchronization frequency in a particular way they characterize the importance of nodes in a network and the relations between them expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale free random networks and for a erdos renyi random network we briefly discuss an application of the perturbation theory in the second order to network structural analysis

a lyapunov proof of an improved maximum allowable transfer interval for networked control systems simple lyapunov proofs are given for an improved relative to previous results that have appeared in the literature bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval

value iteration and adaptive dynamic programming for data driven adaptive optimal control design this paper presents a novel non model based data driven adaptive optimal controller design for linear continuous time systems with completely unknown dynamics inspired by the stochastic approximation theory a continuous time version of the traditional value iteration vi algorithm is presented with rigorous convergence analysis this vi method is crucial for developing new adaptive dynamic programming methods to solve the adaptive optimal control problem and the stochastic robust optimal control problem for linear continuous time systems fundamentally different from existing results the a priori knowledge of an initial admissible control policy is no longer required the efficacy of the proposed methodology is illustrated by two examples and a brief comparative study between vi and earlier policy iteration methods

adaptive neural network based event triggered control of single input single output nonlinear discrete time systems this paper presents a novel adaptive neural network nn control of single input and single output uncertain nonlinear discrete time systems under event sampled nn inputs in this control scheme the feedback signals are transmitted and the nn weights are tuned in an aperiodic manner at the event sampled instants after reviewing the nn approximation property with event sampled inputs an adaptive state estimator se consisting of linearly parameterized nns is utilized to approximate the unknown system dynamics in an event sampled context the se is viewed as a model and its approximated dynamics and the state vector during any two events are utilized for the event triggered controller design an adaptive event trigger condition is derived by using both the estimated nn weights and a dead zone operator to determine the event sampling instants this condition both facilitates the nn approximation and reduces the transmission of feedback signals the ultimate boundedness of both the nn weight estimation error and the system state vector is demonstrated through the lyapunov approach as expected during an initial online learning phase events are observed more frequently over time with the convergence of the nn weights the inter event times increase thereby lowering the number of triggered events these claims are illustrated through the simulation results

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

gaussian noise and the two network frustrated kuramoto model abstract we examine analytically and numerically a variant of the stochastic kuramoto model for phase oscillators coupled on a general network two populations of phased oscillators are considered labelled blue and red each with their respective networks internal and external couplings natural frequencies and frustration parameters in the dynamical interactions of the phases we disentangle the different ways that additive gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a laplacian decomposition for the sub graphs for blue and red under the linearisation ansatz that the oscillators of each respective network remain relatively phase synchronised centroids or clusters we are able to obtain simple closed form expressions using the fokker planck approach for the dynamics of the average angle of the two centroids in some cases this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials these considerations are extended to a regime where one of the populations has fragmented in two the analytic expressions we derive largely predict the dynamics of the non linear system seen in numerical simulation in particular we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented

lq optimal sampled data control under stochastic delays gridding approach for stabilizability and detectability we solve a linear quadratic optimal control problem for sampled data systems with stochastic delays the delays are stochastically determined by the last few delays the proposed optimal controller

q learning for continuous time linear systems a model free infinite horizon optimal control approach abstract in this paper we propose an online q learning algorithm to solve the infinite horizon optimal control problem of a linear time invariant system with completely uncertain unknown dynamics we first formulate the q function by using the hamiltonian and the optimal cost an integral reinforcement learning approach is used to develop an actor critic approximator structure to estimate the parameters of the q function online while also guaranteeing closed loop asymptotic stability and convergence to the optimal solution

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

collective phase description of globally coupled excitable elements we develop a theory of collective phase description for globally coupled noisy excitable elements exhibiting macroscopic oscillations collective phase equations describing macroscopic rhythms of the system are derived from langevin type equations of globally coupled active rotators via a nonlinear fokker planck equation the theory is an extension of the conventional phase reduction method for ordinary limit cycles to limit cycle solutions in infinite dimensional dynamical systems such as the time periodic solutions to nonlinear fokker planck equations representing macroscopic rhythms we demonstrate that the type of the collective phase sensitivity function near the onset of collective oscillations crucially depends on the type of the bifurcation namely it is type i for the saddle node bifurcation and type ii for the hopf bifurcation