Stochastic complex networks synchronize to the limit set with adaptive controller and adaptive delay
Corresponding Author
Yuhua Xu
Department of Mathematics and Finance, Yunyang Teachers' College, Hubei, Shiyan 442000, China
Computer School of Wuhan University, Wuhan 430079, China
Correspondence to: Yuhua Xu, Department of Mathematics and Finance, Yunyang Teachers' College, Hubei, Shiyan 442000, China.
Yuling Wang, School of Economics, South-Central University for Nationalities, Wuhan 430074, China.
E-mail: [email protected]; [email protected]
Search for more papers by this authorYuling Wang
School of Economics, South-Central University for Nationalities, Wuhan 430074, China
Search for more papers by this authorWuneng Zhou
College of Information Science and Technology, Donghua University, Shanghai 201620, China
Search for more papers by this authorJian'an Fang
College of Information Science and Technology, Donghua University, Shanghai 201620, China
Search for more papers by this authorCorresponding Author
Yuhua Xu
Department of Mathematics and Finance, Yunyang Teachers' College, Hubei, Shiyan 442000, China
Computer School of Wuhan University, Wuhan 430079, China
Correspondence to: Yuhua Xu, Department of Mathematics and Finance, Yunyang Teachers' College, Hubei, Shiyan 442000, China.
Yuling Wang, School of Economics, South-Central University for Nationalities, Wuhan 430074, China.
E-mail: [email protected]; [email protected]
Search for more papers by this authorYuling Wang
School of Economics, South-Central University for Nationalities, Wuhan 430074, China
Search for more papers by this authorWuneng Zhou
College of Information Science and Technology, Donghua University, Shanghai 201620, China
Search for more papers by this authorJian'an Fang
College of Information Science and Technology, Donghua University, Shanghai 201620, China
Search for more papers by this authorAbstract
This paper investigates the problem of two stochastic complex networks synchronize to the limit set with adaptive controller and adaptive delay, which are not fully considered in the existing research. A few articles on stability of stochastic complex networks with time-varying delay is discussed, but the time-varying delayed and its derivative are bounded on time t. In this paper, the time-varying delay is adaptive. Also, the coupling matrix with stochastic perturbation is also considered. Copyright © 2013 John Wiley & Sons, Ltd.
References
- 1 Strogatz S. Exploring complex networks. Nature 2001; 410: 268–276.
- 2 Li X, Chen G. Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Transactions on Circuits and Systems—I: Fundamental Theory and Applications 2003; 50: 1381–1390.
- 3 Yu W, Cao J. Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification. Physica A 2007; 375: 467–482.
- 4 Zhou J, Xiang L, Liu Z. Global synchronization in general complex delayed dynamical networks and its applications. Physica A 2007; 385: 729–742.
- 5 Wang H, Ding C. Impulsive control for differential systems with delay. Mathematical Methods In The Applied Sciences 2013; 36: 967–973.
- 6 Xi Q. Global exponential stability for a class of generalized delayed neural networks with impulses. Mathematical Methods In The Applied Sciences 2011; 34: 1414–1420.
- 7 Wu X. Synchronization-based topology identification of weighted general complex dynamical networks with time varying coupling delay. Physica A 2008; 387: 997–1008.
- 8 Zhang Q, Lu J, Lü J, Tse C. Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Transactions on Circuits and Systems—II: Express Briefs 2008; 55: 183–187.
- 9 Feng J, Sun S, Xu C, Zhao Y, Wang J. The synchronization of general complex dynamical network via pinning control. Nonlinear Dynamics 2012; 67: 1623–1633.
- 10 Yu W. A LMI-based approach to global asymptotic stability of neural networks with time varying delays. Nonlinear Dynamics 2007; 48: 165–174.
- 11 Pan L, Cao J. Stochastic quasi-synchronization for delayed dynamical networks via intermittent control. Communications in Nonlinear Science and Numerical Simulation 2012; 17: 1332–1343.
- 12 Tang Y, Wong W. Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Transactions On Neural Networks and Learning Systems 2013; 24: 435–447.
- 13 Tang Y, Gao H, Zou W, Kurths J. Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Transactions On Cybernetics 2013; 43: 358–370.
- 14 Tang Y, Wang Z, Gao H, Swift S, Kurths J. A constrained evolutionary computation method for detecting controlling regions of cortical networks. IEEE/ACM Transactions On Computational Biology and Bioinformatics 2012; 9: 1569–1581.
- 15 Tang Y, Fang J, Xia M, Gu X.Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays. Applied Mathematical Modelling 2010; 34: 843–855.
- 16 Tang Y, Qiu R, Fang J, Miao Q, Xia M. Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Physics Letters A 2008; 372: 4425–4433.
- 17 Zhou J, Chen T, Xiang L. Chaotic lag synchronization of coupled delayed neural networks and its applications in secure communication. Circuits, Systems, and Signal Processing 2005; 24: 599–613.
- 18 Li X, Cao J. Adaptive synchronization for delayed neural networks with stochastic perturbation. Journal of the Franklin Institute 2008; 354: 779–791.
- 19 Zhu Q, Cao J. Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays. Communications in Nonlinear Science and Numerical Simulation 2011; 16: 2139–2159.
- 20 Liu Z, Lü S, Zhong S, Ye M. pth moment exponential synchronization analysis for a class of stochastic neural networks with mixed delays. Communications in Nonlinear Science and Numerical Simulation 2010; 15: 1899–1909.
- 21 Botmart T, Niamsup P, Liu X. Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Communications in Nonlinear Science and Numerical Simulation 2012; 17: 1894–1907.
- 22 Sun Y, Cao J. pth moment exponential stability of stochastic recurrent neural networks with time-varying delays. Nonlinear Analysis: Real World Applications 2007; 8: 1171–1185.
- 23 Zhu Q, Cao J. pth moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching. Nonlinear Dynamics 2012; 67: 829–845.
- 24 Huang C, He Y, Huang L, Zhu W. pth moment stability analysis of stochastic recurrent neural networks with time-varying delays. Information Sciences 2008; 178: 2194–2203.
- 25 Wang X, Guo Q, Xu D. Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. Mathematics and Computers in Simulation 2009; 79: 1698–1710.
- 26 Mao X. A note on the laSalle-type theorems for stochastic differential delay equations. Journal of Mathematical Analysis and Applications 2002; 268: 125–142.
- 27 Huang C, Cao J. On pth moment exponential stability of stochastic Cohen–Grossberg neural networks with timevarying delays. Neurocomputing 2010; 73: 986–990.