decentralised consensus based formation tracking of multiple differential drive robots abstractthis article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange a class of general state and input transform is introduced to convert the formation tracking issue of multi robot systems into the consensus like problem with time varying reference the distributed observer based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory the finite time stability of observer and control law is analysed rigorously by using the lyapunov direct method algebraic graph theory and matrix analysis numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper

stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling in this paper stochastic resonance of an ensemble of coupled bistable systems driven by noise having an stable distribution and nonhomogeneous coupling is investigated the stable distribution considered here is characterized by four intrinsic parameters 0 2 is called the stability parameter for describing the asymptotic behavior of stable densities 1 1 is a skewness parameter for measuring asymmetry 0 is a scale parameter for measuring the width of the distribution and is a location parameter for representing the mean value it is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths we show that the stability parameter and the scale parameter can be well selected to generate resonant effects in response to external signals in addition the interplay between the skewness parameter and the location parameter on the resonance effects is also studied we further show that the asymmetry of a l evy stable distribution resulting from the skewness parameter and the location parameter can enhance the resonance effects both theoretical analysis and simulation are presented to verify the results of this paper

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

synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

robust stability and stabilisation of 2d discrete state delayed systems abstract in this paper we first present sufficient stability and robust stability conditions for discrete linear state delayed 2d systems in terms of linear matrix inequalities all results are obtained with fornasini marchesini delay model but appropriate transformation to the corresponding roesser form is provided as well generalisation to the multiple state delayed case is also given then the stabilisation and robust stabilisation using static state feedback are studied stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities an numerical example is used to illustrate the effectiveness of the approach

synchronization via pinning control on general complex networks this paper studies synchronization via pinning control on general complex dynamical networks such as strongly connected networks networks with a directed spanning tree weakly connected networks and directed forests a criterion for ensuring network synchronization on strongly connected networks is given it is found that the vertices with very small in degrees should be pinned first in addition it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers which implies that the vertices with very large out degrees may be pinned then a criterion for achieving synchronization on networks with a directed spanning tree which can be composed of many strongly connected components is derived it is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls

on a new class of t norms and t conorms on bounded lattices abstract the ordinal sum of triangular norms on unit interval has been used to construct other triangular norms but in general ordinal sum construction of triangular norms and triangular conorms may not work on an arbitrary bounded lattice in this study we focus on ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice moreover we show a complete generalization of our ordinal sums of triangular norms and triangular conorms on an arbitrary bounded lattice and some illustrative examples are added for clarity

a family of strict and discontinuous triangular norms answers to some questions about triangular norms are given precisely a procedure of construction of infinitely many triangular norms is obtained one for each operation n2 n such that n is a strictly ordered commutative semigroup each of them is discontinuous at each point of a dense subset of 0 1 2 and it satisfies the condition t kx y t x ky for infinitely many k 0 1

pinning impulsive synchronization of reaction diffusion neural networks with time varying delays this paper investigates the exponential synchronization of reaction diffusion neural networks with time varying delays subject to dirichlet boundary conditions a novel type of pinning impulsive controllers is proposed to synchronize the reaction diffusion neural networks with time varying delays by applying the lyapunov functional method sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction diffusion neural networks with large and small delay sizes it is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network the technique used in this paper is also applicable to reaction diffusion networks with neumann boundary conditions numerical examples are presented to demonstrate the effectiveness of the theoretical results

positive real control of two dimensional systems roesser models and linear repetitive processes this paper considers the problem of positive real control for two dimensional 2 d discrete systems described by the roesser model and also discrete linear repetitive processes which are another distinct sub class of 2 d linear systems of both systems theoretic and applications interest the purpose of this paper is to design a dynamic output feedback controller such that the resulting closed loop system is asymptotically stable and the closed loop system transfer function from the disturbance to the controlled output is extended strictly positive real we first establish a version of positive realness for 2 d discrete systems described by the roesser state space model then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four lmis when these lmis are feasible an explicit parameterization of the desired output feedback controllers is given we then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1 d state space form finally we provide numerical examples to demonstrate the applicability of the approach

duality for a class of binary operations on 0 1 abstract in this paper we study a duality relation for pairs of a class of binary operations on 0 1 from the solution of a functional equation system solved by de rham in 1956 we obtain several results finally by using a dense set in 0 1 a description of the key function in this work is obtained

desynchronization waves in small world networks a regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased due to the spread of localized instability of eigenvectors of the laplacian matrix we find that shortcuts which make a regular network small world can destroy ordered desynchronization wave patterns wave patterns in a small world network are usually destroyed gradually as the degree of regularity in the network deteriorates no ordered wave patterns are observed in scale free and random networks the formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator we derive a general type of the kardar parisi zhang equation for phase evolution in a prototype oscillator network the equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise

synchronization transitions on scale free neuronal networks due to finite information transmission delays we investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale free neuronal networks with different average degrees and scaling exponents as the underlying model of neuronal dynamics we use the efficient rulkov map with additive noise we show that increasing the coupling strength enhances synchronization monotonously whereas delay plays a more subtle role in particular we found that depending on the inherent oscillation frequency of individual neurons regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases these delay induced synchronization transitions manifest as well expressed minima in the measure for spatial synchrony appearing at every multiple of the oscillation frequency larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization these results are robust against variations in system size intensity of additive noise and the scaling exponent of the underlying scale free topology we argue that fine tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and indeed they should be seen as important as the coupling strength or the overall density of interneuronal connections we finally discuss some biological implications of the presented results

on the nonexistence of quadratic lyapunov functions for consensus algorithms we provide an example proving that there exists no quadratic lyapunov function for a certain class of linear agreement consensus algorithms a fact that had been numerically verified in we also briefly discuss sufficient conditions for the existence of such a lyapunov function

distributed consensus for sampled data control multi agent systems with missing control inputs abstract this paper is concerned about the distributed consensus problem for general sampled data control multi agent systems without or with a leader under control inputs missing over some sampling intervals for these two cases a distributed adaptive dynamical consensus algorithm is proposed based only on the relative information of network structure under the assumption that the dynamical network contains a directed spanning tree some sufficient consensus conditions are induced under a switched model these obtained consensus criteria are independent of dynamical network topology namely they are valid for both undirected and directed topology besides they do not rely on the spectra and the eigenvalue of laplacian matrix furthermore some quantitative relations included in dynamical systems such as sampling period admissible control inputs missing rate and exponential reaching rate of the consensus performance are established finally simulation examples are given to show the effectiveness of the proposed results

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

hopf bifurcation of an n 1 neuron bidirectional associative memory neural network model with delays recent studies on hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two three four five or six neurons it is well known that neural networks are complex and large scale nonlinear dynamical systems so the dynamics of the delayed neural networks are very rich and complicated although discussing the dynamics of networks with a few neurons may help us to understand large scale networks there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large scale networks in this paper a general delayed bidirectional associative memory neural network model with n 1 neurons is considered by analyzing the associated characteristic equation the local stability of the trivial steady state is examined and then the existence of the hopf bifurcation at the trivial steady state is established by applying the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution furthermore the paper highlights situations where the hopf bifurcations are particularly critical in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections it is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons numerical simulations are carried out to illustrate the main results

bifurcations in a delayed fractional complex valued neural network complex valued neural networks cvnns with integer order have attracted much attention and which have been well discussed fractional complex valued neural networks fcvnns are more suitable to describe the dynamical properties of neural networks but have rarely been studied it is the first time that the stability and bifurcation of a class of delayed fcvnn is investigated in this paper the activation function can be expressed by separating into its real and imaginary parts by using time delay as the bifurcation parameter the dynamical behaviors that including local asymptotical stability and hopf bifurcation are discussed the conditions of emergence of bifurcation are obtained furthermore it reveals that the onset of the bifurcation point can be delayed as the order increases finally an illustrative example is provided to verify the correctness of the obtained theoretical results

lmi stability tests for the fornasini marchesini model we present a linear matrix inequality lmi for testing the stability of a 2 d system described by the fornasini marchesini first model the test is based on the properties of sum of squares polynomials with matrix coefficients although the test implements a sufficient condition extensive experiments suggest that the gap to necessity is very small we also derive an lmi describing stability conditions around a given model and useful in robust stability testing

pseudo analysis and its applications in railway routing using as a base the pseudo analysis the problem of railway routing is treated first a deterministic approach is applied on three and four stations these problems are treated also with a stochastic approach when one variable is randomized

model approximation for switched genetic regulatory networks the model approximation problem is studied in this paper for switched genetic regulatory networks grns with time varying delays we focus on constructing a reduced order model to approximate the high order grns considered under the switching signal subject to certain constraints such that the approximation error system between the original and reduced order systems is exponentially stable with a disturbance attenuation performance the stability conditions and the disturbance attenuation performance are established by utilizing two integral inequality bounding techniques and the average dwell time method for the approximation error system then the solvability conditions for the reduced order models for the grns are also established using the projection method furthermore the model approximation problem can be transferred into a sequential minimization problem that is subject to linear matrix inequality constraints by using the cone complementarity algorithm finally several examples are provided to illustrate the effectiveness and the advantages of the proposed methods

a characterization of the hamacher family of t norms abstract starting from a fuzzy conjunction there are two main ways of defining a fuzzy implication operator a functional equation for t norms is obtained and studied which describes the equality of these two implications when the underlying conjunction has a particular form defined from a t norm the solution makes clear that this functional equation together with an additional condition provides a complete characterization of the hamacher family of t norms having positive parameter

idempotent nullnorms on bounded lattices abstract nullnorms are generalizations of triangular norms and triangular conorms with a zero element to be an arbitrary point from a bounded lattice in this paper we study and discuss the existence of idempotent nullnorms on bounded lattices considering an arbitrary distributive bounded lattice l we show that there exists a unique idempotent nullnorm on l we prove that an idempotent nullnorm may not always exist on an arbitrary bounded lattice furthermore we propose a construction method to obtain idempotent nullnorms on a bounded lattice l with an additional constraint on a for the given zero element a l 0 1

generalized toda brackets and equivariant moore spectra in this paper we develop a general theory of obstructions to the existence of equivariant moore spectra the obstructions we obtain coincide with higher order toda brackets as defined by spanier we then apply the theory to show the existence of equivariant moore spectra in various special cases

cluster delay consensus in multi agent systems via pinning leader following approach with intermittent effect abstractin this paper the cluster consensus problem with delays of first order nonlinear multi agent systems is studied through pinning leader following approach with periodic intermittent effect the graph of the networked system is assumed to be directed and weakly connected a new type of pinning consensus protocol with intermittent effect is designed according to the ways in which the agents link specifically the agents in each cluster are divided into three subsets due to the orientation of their topological degree and each subset of agents is controlled by an individual law a redefined notion on cluster consensus with two sorts of time delays is proposed in this article some consensus criteria are derived to guarantee that the agents in the same cluster asymptotically follow the virtual leader with a delay while agents in different clusters reach consensus with delays via following their leaders some numerical simulations are given to illustrate the effectiveness of the theoretical results

synchronization control for discrete time delayed dynamical networks with switching topology under actuator saturations this article is concerned with the synchronization control problem for a class of discrete time dynamical networks with mixed delays and switching topology the saturation phenomenon of physical actuators is specifically considered in designing feedback controllers by exploring the mixed delay dependent sector conditions in combination with the piecewise lyapunov like functional and the average dwell time switching a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances while the l l performance constraint is satisfied furthermore the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances second by using some congruence transformations the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities then three convex optimization problems are formulated regarding the disturbance tolerance the l l performance and the initial condition set respectively finally two simulation examples are given to show the effectiveness and merits of the proposed results

optimal design for synchronization of cooperative systems state feedback observer and output feedback this technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree a leader node or command generator is considered which generates the desired tracking trajectory a framework for cooperative tracking control is proposed including full state feedback control observer design and dynamic output feedback control the classical system theory notion of duality is extended to networked systems it is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

influence of time delayed feedback in the firing pattern of thermally sensitive neurons we explore the dynamics of a hodgkin huxley type model for thermally sensitive neurons that exhibit intrinsic oscillatory activity the model is modified to include a feedback loop that is represented by two parameters the synaptic strength and the transmission delay time we analyze the dynamics of the neuron depending on the temperature the synaptic strength and the delay time we find parameter regions where the effect of the recurrent connexion is excitatory inducing spikes or trains of spikes and regions where it is inhibitory reducing or eliminating completely the spiking behavior we characterize the complex interplay of the intrinsic dynamics of the neuron with the recurrent feedback input and a noisy input

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

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

existence and stability of almost periodic solutions for cellular neural networks with time varying delays in leakage terms on time scales abstract this paper is concerned with cellular neural networks with time varying delays in leakage terms on time scales some sufficient conditions on the existence uniqueness and global exponential stability of almost periodic solutions are established an example is presented to illustrate the feasibility and effectiveness of the obtained results

global h_ infty pinning synchronization of complex networks with sampled data communications this paper investigates the global h infty pinning synchronization problem for a class of complex networks with aperiodic samplings combined with the writinger based integral inequality a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network furthermore a novel condition is proposed under which the complex network is globally pinning synchronized with a given h infty performance index it is shown that the h infty performance index gamma has a positive correlation with the upper bound of the sampling intervals finally the validity and the advantage of the theoretic results obtained are verified by means of the applications in chua s circuit and pendulum

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

mathematical modeling of tumor immune competitive system considering the role of time delay abstract in this paper we consider a three dimensional nonlinear delay differential system tumor cells cytotoxic t lymphocytes t helper cells with single interaction delay we perform linear stability of the equilibria and the existence of hopf bifurcation in which the discrete time delay is used as a bifurcation parameter we estimate the length of delay to preserve the stability of period 1 limit cycle we also investigate the direction period and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory we observe that the discrete time delay plays an important role in stability switching numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay including the existence of periodic oscillations which demonstrate the phenomena of long term tumor relapse

on a new class of uninorms on bounded lattices we study and propose some new construction methods to obtain uninorms on bounded lattices considering an arbitrary bounded lattice l we show the existence of idempotent uninorms on l for any element e l 0 1 playing the role of a neutral element by our construction method we obtain the smallest idempotent uninorm and the greatest idempotent uninorm with the neutral element e l 0 1 we see that the obtained uninorms are conjunctive and disjunctive uninorms respectively on the other hand if l is not a chain we also provide an example of an idempotent uninorm which is neither conjunctive nor disjunctive

representation of nullnorms on bounded lattices abstract recently nullnorms on bounded lattices have been frequently investigated by many researchers in this paper we give the full characterization for quite a general class of nullnorms on bounded lattices and represent them by their underlying t norms and t conorms an example is given to show the relationship between each block of the nullnorms we also fully determine the values of arbitrary nullnorms when only one of the two variables is comparable with the absorbing elements for the rest cases we give some necessary conditions

robust synchronization for 2 d discrete time coupled dynamical networks in this paper a new synchronization problem is addressed for an array of 2 d coupled dynamical networks the class of systems under investigation is described by the 2 d nonlinear state space model which is oriented from the well known fornasini marchesini second model for such a new 2 d complex network model both the network dynamics and the couplings evolve in two independent directions a new synchronization concept is put forward to account for the phenomenon that the propagations of all 2 d dynamical networks are synchronized in two directions with influence from the coupling strength the purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm bounded or the polytopic parameter uncertainties an energy like quadratic function is developed together with the intensive use of the kronecker product to establish the easy to verify conditions under which the addressed 2 d complex network model achieves global synchronization finally a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme

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

stability and bifurcation analysis of delay induced tumor immune interaction model a modified mathematical model of kuznetsov et al 1994 representing tumor immune interaction with discrete time delay is proposed in this paper by choosing the discrete time delay as the bifurcation parameter we establish the sufficient condition for local stability of interior steady state hopf bifurcation occurs when the time delay passes a critical value the estimation of the length of delay to preserve stability has been derived moreover based on the normal form theory and center manifold theorem we establish explicit expressions to determine the direction of hopf bifurcation and the stability of bifurcating periodic solutions numerical simulations are obtained to validate our analytical findings by varying the system parameter a two parameters bifurcation diagrams are also shown by varying the system parameters which bring out the rich biological dynamics of the system

hopf bifurcation for neutral type neural network model with two delays in this paper the dynamics of a neutral neural network model with two delays is investigated the condition to ensure the stability of the zero solution of the system is decided by choosing 1 and 2 as parameters respectively then the hopf bifurcation is discussed by using the center manifold theory and normal form method introduced by hassard and kazarinoff global existence of periodic solution is studied by using the global hopf bifurcation theory finally some numerical simulations are carried out to illustrate the analytical results

pinning synchronization of directed networks with switching topologies a multiple lyapunov functions approach this paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies the common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper using tools from m matrix theory and stability analysis of the switched nonlinear systems a new kind of network topology dependent multiple lyapunov functions is proposed for analyzing the synchronization behavior of the whole network it is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed finally some numerical simulations on coupled neural networks are provided to verify the theoretical results

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

h sub spl infin filtering of 2 d discrete systems this paper deals with h sub spl infin filtering of two dimensional 2 d linear discrete systems described by a 2 d local state space lss fornasini marchesini 1978 second model several versions of the bounded real lemma of the 2 d discrete systems are established the 2 d bounded real lemma allows us to solve the finite horizon and infinite horizon h sub spl infin filtering problems using a riccati difference equation or a riccati inequality approach further a solution to the infinite horizon h sub spl infin filtering problem based on a linear matrix inequality lmi approach is developed our results extend existing work for one dimensional 1 d systems to the 2 d case and give a state space solution to the bounded realness of 2 d discrete systems as well as 2 d h sub spl infin filtering for the first time numerical examples are given to demonstrate the riccati difference equation approach to the 2 d finite horizon h sub spl infin filtering problem and the lmi approach to the 2 d infinite horizon h sub spl infin filtering problem

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

stability and synchronization of discrete time markovian jumping neural networks with mixed mode dependent time delays in this paper we introduce a new class of discrete time neural networks dnns with markovian jumping parameters as well as mode dependent mixed time delays both discrete and distributed time delays specifically the parameters of the dnns are subject to the switching from one to another at different times according to a markov chain and the mixed time delays consist of both discrete and distributed delays that are dependent on the markovian jumping mode we first deal with the stability analysis problem of the addressed neural networks a special inequality is developed to account for the mixed time delays in the discrete time setting and a novel lyapunov krasovskii functional is put forward to reflect the mode dependent time delays sufficient conditions are established in terms of linear matrix inequalities lmis that guarantee the stochastic stability we then turn to the synchronization problem among an array of identical coupled markovian jumping neural networks with mixed mode dependent time delays by utilizing the lyapunov stability theory and the kronecker product it is shown that the addressed synchronization problem is solvable if several lmis are feasible hence different from the commonly used matrix norm theories such as the m matrix method a unified lmi approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation where the lmis can be easily solved by using the available matlab lmi toolbox two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

partial nodes based state estimation for complex networks with unbounded distributed delays in this brief the new problem of partial nodes based pnb state estimation problem is investigated for a class of complex network with unbounded distributed delays and energy bounded measurement noises the main novelty lies in that the states of the complex network are estimated through measurement outputs of a fraction of the network nodes such fraction of the nodes is determined by either the practical availability or the computational necessity the pnb state estimator is designed such that the error dynamics of the network state estimation is exponentially ultimately bounded in the presence of measurement errors sufficient conditions are established to ensure the existence of the pnb state estimators and then the explicit expression of the gain matrices of such estimators is characterized when the network measurements are free of noises the main results specialize to the case of exponential stability for error dynamics numerical examples are presented to verify the theoretical results

global asymptotic stability of stochastic bam neural networks with distributed delays and reaction diffusion terms this paper is concerned with global asymptotic stability of a class of reaction diffusion stochastic bi directional associative memory bam neural networks with discrete and distributed delays based on suitable assumptions we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for reaction diffusion stochastic bam neural networks with discrete and distributed delays the obtained results are easy to check and improve upon the existing stability results an example is also given to demonstrate the effectiveness of the obtained results

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

exponential synchronization of neural networks with discrete and distributed delays under time varying sampling this paper investigates the problem of master slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals an improved method is proposed which captures the characteristic of sampled data systems some delay dependent criteria are derived to ensure the exponential stability of the error systems and thus the master systems synchronize with the slave systems the desired sampled data controller can be achieved by solving a set of linear matrix inequalitys which depend upon the maximum sampling interval and the decay rate the obtained conditions not only have less conservatism but also have less decision variables than existing results simulation results are given to show the effectiveness and benefits of the proposed methods

stability of synchronous oscillations in a system of hodgkin huxley neurons with delayed diffusive and pulsed coupling we study the synchronization dynamics for a system of two hodgkin huxley hh neurons coupled diffusively or through pulselike interactions by calculating the maximum transverse lyapunov exponent we found that with diffusive coupling there are three regions in the parameter space corresponding to qualitatively distinct behaviors of the coupled dynamics in particular the two neurons can synchronize in two regions and desynchronize in the third when excitatory and inhibitory pulse coupling is considered we found that synchronized dynamics becomes more difficult to achieve in the sense that the parameter regions where the synchronous state is stable are smaller numerical simulations of the coupled system are presented to validate these results the stability of a network of coupled hh neurons is then analyzed and the stability regions in the parameter space are exactly obtained

stochastic resonance in a tumor immune system subject to bounded noises and time delay abstract immunotherapy is one of the most recent approaches in cancer therapy a mathematical model of tumor immune interaction subject to a periodic immunotherapy treatment imitated by a periodic signal correlative and bounded stochastic fluctuations and time delays is investigated by numerical simulations for its signal power amplification spa within the tailored parameter regime the synchronous response of tumor growth to the immunotherapy stochastic resonance sr versus both the noises and delays is obtained the details are as follows i the peak values of spa versus the noise intensity a in the proliferation term of tumor cells decrease as the frequency of periodic signal increases i e an increase of the frequency restrains the sr ii an increase of the amplitude of periodic signal restrains the sr versus a but boosts up the sr versus the noise intensity b in the immune term iii there is an optimum cross correlated degree between the two bounded noises at which the system exhibits the strongest sr versus the delay time the reaction time of tumor cell population to their surrounding environment constraints iv upon increasing the delay time double sr versus the delay time the time taken by both the tumor antigen identification and tumor stimulated proliferation of effectors emerges these results may be helpful for an immunotherapy treatment for the sufferer

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

scale free networks from varying vertex intrinsic fitness a new mechanism leading to scale free networks is proposed in this letter it is shown that in many cases of interest the connectivity power law behavior is neither related to dynamical properties nor to preferential attachment assigning a quenched fitness value x i to every vertex and drawing links among vertices with a probability depending on the fitnesses of the two involved sites gives rise to what we call a good get richer mechanism in which sites with larger fitness are more likely to become hubs i e to be highly connected

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

synchronization transition in scale free networks clusters of synchrony we study the synchronization transition in scale free networks that display power law asymptotic behaviors in their degree distributions the critical coupling strength and the order parameter critical exponent derived by the mean field approach depend on the degree exponent ensuremath lambda which implies a close connection between structural organization and the emergence of dynamical order in complex systems we also derive the finite size scaling behavior of the order parameter finding that the giant cluster of synchronized nodes is formed in different ways between scale free networks with 2l ensuremath lambda l3 and those with ensuremath lambda g3

experimental confirmation of chaotic phase synchronization in coupled time delayed electronic circuits we report the experimental demonstration of chaotic phase synchronization cps in unidirectionally coupled time delay systems using electronic circuits we have also implemented experimentally an efficient methodology for characterizing cps namely the localized sets snapshots of the evolution of coupled systems and the sets as observed from the oscilloscope confirming cps are shown experimentally numerical results from different approaches namely phase differences localized sets changes in the largest lyapunov exponents and the correlation of probability of recurrence c cpr corroborate the experimental observations

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

nullnorms on bounded lattices derived from t norms and t conorms abstract nullnorms with an annihilator a in any point of a bounded lattice are generalizations and unifications of t norms and t conorms this study continues to investigate the construction of nullnorms on bounded lattices we propose some methods to construct nullnorms derived from t norms and t conorms on bounded lattices where some sufficient and necessary conditions on theirs annihilator are required as a by product of these constructions idempotent nullnorms on bounded lattices are obtained further we provide some illustrative examples of the new classes of nullnorms idempotent nullnorms on bounded lattices

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

switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation one dimensional models are important for developing demonstrating and testing new methods and approaches which can be extended to more complex systems we design for a linear delay differential equation a reliable numerical method which consists of two time splits as follows a it is an exact scheme at the early time evolution t where is the discrete value of the delay b thereafter it is a nonstandard finite difference nsfd scheme obtained by suitable discretizations at the backtrack points it is shown theoretically and computationally that the nsfd scheme is dynamically consistent with respect to the asymptotic stability of the trivial equilibrium solution of the continuous model extension of the nsfd to nonlinear epidemiological models and its good performance are tested on a numerical example

different interpretations of triangular norms and related operations triangular norms and triangular conorms and uni norms can be treated as semigroup two place function also as commutative semiring multiplications it can also be derived from the difference operation in a difference poset we discuss here these different interpretations and their consequences

paths to globally generalized synchronization in scale free networks we apply the auxiliary system approach to study paths to globally generalized synchronization in scale free networks of identical chaotic oscillators including h enon maps logistic maps and lorentz oscillators as the coupling strength ensuremath epsilon between nodes of the network is increased transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds are found the generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of ensuremath epsilon our result is useful for understanding the synchronization process in complex networks

convergence analysis of directed signed networks via an m matrix approach abstractthis paper aims at solving convergence problems on directed signed networks with multiple nodes where interactions among nodes are described by signed digraphs the convergence analysis is

construction methods for idempotent nullnorms on bounded lattices abstract in this paper we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators we introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other in order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm some illustrative examples are added

synchronization processes in complex networks we present an extended analysis based on the dynamics towards synchronization of a system of coupled oscillators of the hierarchy of communities in complex networks in the synchronization process different structures corresponding to well defined communities of nodes appear in a hierarchical way the analysis also provides a useful connection between synchronization dynamics complex networks topology and spectral graph analysis

the control gain region for synchronization in non diffusively coupled complex networks abstract the control gain region for synchronization of non diffusively coupled networks was studied with respect to three conditions synchronization synchronization in finite time and synchronization in the minimum time based on cancellation control methodology and master stability function formalism we found that a complete feasible control gain region may be bounded unbounded empty or a union of several bounded and unbounded regions with a similar shape to the synchronized region an interesting possibility emerged that a network could be synchronized by both negative and positive feedback control simultaneously by bridging synchronizability and synchronizing response speeds with a settling time index we have developed timed synchronized region tsr as a substitute for the classical synchronized region to study finite time synchronization as for the last condition a graphical method was developed to estimate control gain with the minimum synchronization time cgmst each condition has examples provided for illustration and verification

synchronization of oscillators through time shifted common inputs shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems however due to finite signal transmission speeds and differences in the distance to the source time shifts between otherwise common inputs are unavoidable since common inputs can be a source of correlation between the elements of multi unit dynamical systems regardless of whether these elements are directly connected with one another or not it is of importance to understand their impact on synchronization as a canonical model that is representative for a variety of different dynamical systems we study limit cycle oscillators that are driven by stochastic time shifted common inputs we show that if the oscillators are coupled time shifts in stochastic common inputs do not simply shift the distribution of the phase differences but rather the distribution actually changes as a result the best synchronization is therefore achieved at a precise intermediate value of the time shift which is due to a resonance like effect with the most probable phase difference that is determined by the deterministic dynamics

synchronization transition in degenerate optical parametric oscillators induced by nonlinear coupling in this paper the synchronization of certain degenerate optical parametric oscillators is investigated in detail complete and or partial synchronization can be reached when linear controller constructed by the real part or imaginary part of the subharmonic mode is imposed on the chaotic degenerate optical parametric oscillators with appropriate coupling intensity the lyapunov exponents under different coupling coefficients are calculated to find the critical condition for complete synchronization transition from complete synchronization to partial synchronization is observed when nonlinear coupling is introduced into the two chaotic oscillators it is found that synchronization of chaotic oscillators keeps robust when the intensity of the nonlinear coupling is less than the intensity of the linear coupling the complete synchronization state is destructed and transient period for partial synchronization is in certain delay when the intensity of the nonlinear coupling is beyond the intensity of the linear coupling

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

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