Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control.

This paper deals with the synchronization problem of a class of coupled stochastic complex-valued drive-response networks with time-varying delays via aperiodically intermittent adaptive control. Different from the previous works, the intermittent control is aperiodic and adaptive, and the restrictions on the control width and time delay are removed, which lead to a larger application scope for this control strategy. Then, based on the Lyapunov method and Kirchhoff's Matrix Tree Theorem as well as differential inequality techniques, several novel synchronization conditions are derived for the considered model. Specially, impulsive control is also considered, which can be seen as a special case of the aperiodically intermittent control when the control width tends to zero. And the corresponding synchronization criteria are given as well. As an application of the theoretical results, a class of stochastic complex-valued coupled oscillators with time-varying delays is studied, and the numerical simulations are also given to demonstrate the effectiveness of the control strategies.

[1]  Shuiming Cai,et al.  Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control , 2016, Complex..

[2]  Tianping Chen,et al.  Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Automatic Control.

[3]  Yasuhiro Takeuchi,et al.  Global asymptotic behavior in single-species discrete diffusion systems , 1993 .

[4]  Xiaofan Li,et al.  Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control , 2017, Neural Networks.

[5]  Yan Liu,et al.  The stability of stochastic coupled systems with time delays and time-varying coupling structure , 2016, Appl. Math. Comput..

[6]  Zhang Hao,et al.  Synchronization of complex-valued neural network with sliding mode control , 2016 .

[7]  Michael Y. Li,et al.  Global-stability problem for coupled systems of differential equations on networks , 2010 .

[8]  Thomas K. D. M. Peron,et al.  The Kuramoto model in complex networks , 2015, 1511.07139.

[9]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[10]  Ali Kazemy,et al.  Synchronization Criteria for Complex Dynamical Networks with State and Coupling Time‐Delays , 2017 .

[11]  Ke Wang,et al.  A graph‐theoretic approach to stability of neutral stochastic coupled oscillators network with time‐varying delayed coupling , 2014 .

[12]  I. Schwartz,et al.  Complete chaotic synchronization in mutually coupled time-delay systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Tianping Chen,et al.  Synchronization of Linearly Coupled Networks With Delays via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Tianping Chen,et al.  Synchronization of Nonlinear Coupled Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Jitao Sun,et al.  Stability of complex-valued impulsive and switching system and application to the Lü system , 2014 .

[16]  Yanwen Li,et al.  Razumikhin method conjoined with graph theory to input-to-state stability of coupled retarded systems on networks , 2017, Neurocomputing.

[17]  Chunna Zeng,et al.  Adaptive exponential synchronization of complex-valued Cohen-Grossberg neural networks with known and unknown parameters , 2017, Neural Networks.

[18]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[19]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[20]  Xiaohua Ding,et al.  Razumikhin method to global exponential stability for coupled neutral stochastic delayed systems on networks , 2017 .

[21]  Jinde Cao,et al.  Synchronization of fractional-order complex-valued neural networks with time delay , 2016, Neural Networks.

[22]  Zhidong Teng,et al.  Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. , 2010, Chaos.

[23]  Q. Gan.  Exponential synchronization of generalized neural networks with mixed time-varying delays and reaction-diffusion terms via aperiodically intermittent control. , 2017, Chaos.

[24]  Xuerong Mao,et al.  Robust stability and controllability of stochastic differential delay equations with Markovian switching , 2004, Autom..

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

[26]  Chuandong Li,et al.  Synchronization of chaotic systems with delay using intermittent linear state feedback. , 2008, Chaos.

[27]  Wenxue Li,et al.  Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete‐time state observations , 2018 .

[28]  Bing Chen,et al.  Synchronization of stochastic coupled systems via feedback control based on discrete-time state observations , 2017 .

[29]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Wei Zhang,et al.  Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control , 2015, Neural Networks.

[31]  Guanrong Chen,et al.  Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback , 2009 .

[32]  Jian-an Wang,et al.  Synchronization of delayed complex dynamical network with hybrid-coupling via aperiodically intermittent pinning control , 2017, J. Frankl. Inst..

[33]  Tohru Nitta,et al.  Solving the XOR problem and the detection of symmetry using a single complex-valued neuron , 2003, Neural Networks.

[34]  Ke Wang,et al.  Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching , 2015 .

[35]  Zhidong Teng,et al.  Exponential synchronization for reaction-diffusion networks with mixed delays in terms of p-norm via intermittent driving , 2012, Neural Networks.

[36]  Bin Hu,et al.  Cluster Synchronization of Coupled Genetic Regulatory Networks With Delays via Aperiodically Adaptive Intermittent Control , 2017, IEEE Transactions on NanoBioscience.

[37]  Jitao Sun,et al.  Stability of complex-valued impulsive system with delay , 2014, Appl. Math. Comput..

[38]  Ciann-Dong Yang,et al.  Stability and quantization of complex-valued nonlinear quantum systems , 2009 .

[39]  Hao Zhang,et al.  Complex projective synchronization of complex-valued neural network with structure identification , 2017, J. Frankl. Inst..

[40]  Xinsong Yang,et al.  Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations , 2017, Neural Processing Letters.

[41]  Haijun Jiang,et al.  Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control , 2017, J. Frankl. Inst..

[42]  Jinde Cao,et al.  Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions , 2017, Neural Networks.

[43]  Quan Yin,et al.  Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay , 2014, Neural Processing Letters.

[44]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[45]  Jan Ubøe.  Complex valued multiparameter stochastic integrals , 1995 .

[46]  J. Kurths,et al.  Outer synchronization of coupled discrete-time networks. , 2009, Chaos.