Finite-time synchronization of complex networks with nonidentical discontinuous nodes

In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.

[1]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[2]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[3]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[4]  Sanjay P. Bhat,et al.  Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks , 2008, IEEE Transactions on Automatic Control.

[5]  Tianping Chen,et al.  Adaptive Synchronization of Coupled Chaotic Delayed Systems Based on Parameter Identification and its Applications , 2006, Int. J. Bifurc. Chaos.

[6]  Diyi Chen,et al.  Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme , 2012 .

[7]  Lada A. Adamic,et al.  Internet: Growth dynamics of the World-Wide Web , 1999, Nature.

[8]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Antonio M. Batista,et al.  Delayed feedback control of bursting synchronization in a scale-free neuronal network , 2010, Neural Networks.

[10]  Ray Brown.  Generalizations of the Chua equations , 1993 .

[11]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[12]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[13]  Jinde Cao,et al.  Synchronization of Randomly Coupled Neural Networks With Markovian Jumping and Time-Delay , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  S. M. Lee,et al.  Secure communication based on chaotic synchronization via interval time-varying delay feedback control , 2011 .

[15]  Lihong Huang,et al.  Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations , 2011, Neurocomputing.

[16]  Jinde Cao,et al.  Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches , 2011, Neural Networks.

[17]  Jinde Cao,et al.  Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Bo Liu,et al.  New conditions on synchronization of networks of linearly coupled dynamical systems with non-Lipschitz right-hand sides , 2012, Neural Networks.

[19]  S. Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1987 .

[20]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[21]  Xinzhi Liu,et al.  Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations , 2012, Inf. Sci..

[22]  Ling Lü,et al.  Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network , 2011 .

[23]  Jinde Cao,et al.  Adaptive Lag Synchronization for Competitive Neural Networks With Mixed Delays and Uncertain Hybrid Perturbations , 2010, IEEE Transactions on Neural Networks.

[24]  Habib Dimassi,et al.  A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers , 2012 .

[25]  Ju H. Park,et al.  Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data , 2012 .

[26]  Wenwu Yu,et al.  Quasi-synchronization of Delayed Coupled Networks with Non-identical Discontinuous Nodes , 2012, ISNN.

[27]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[29]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[30]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

[31]  Jinde Cao,et al.  Synchronization of Markovian Coupled Neural Networks With Nonidentical Node-Delays and Random Coupling Strengths , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Chuangxia Huang,et al.  Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations , 2011, Neurocomputing.

[33]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[34]  Guanrong Chen,et al.  Global synchronization and asymptotic stability of complex dynamical networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[35]  Jinde Cao,et al.  Synchronization of delayed complex dynamical networks with impulsive and stochastic effects , 2011 .

[36]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

[37]  Wuquan Li,et al.  Finite-time generalized synchronization of chaotic systems with different order , 2011 .

[38]  Jinde Cao,et al.  Finite-time synchronization of coupled neural networks via discontinuous controllers , 2011, Cognitive Neurodynamics.

[39]  Jinde Cao,et al.  Stochastic synchronization of coupled neural networks with intermittent control , 2009 .

[40]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

[41]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[42]  M. Forti,et al.  Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations , 2006 .

[43]  Marius-F. Danca,et al.  Controlling chaos in discontinuous dynamical systems , 2004 .

[44]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

[45]  Jinde Cao,et al.  Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[46]  Jinde Cao,et al.  Filippov systems and quasi-synchronization control for switched networks. , 2012, Chaos.

[47]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .