Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays

This paper investigates finite-time synchronization of complexed-valued neural networks with multiple time-varying delays and infinite distributed delays. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for finite-time synchronization of the drive-response system based on the new Lyapunov–Krasovskii function and the new analysis techniques. Numerical examples demonstrate the effectiveness of the theoretical results.

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

[2]  Ju H. Park,et al.  Chaos synchronization between two different chaotic dynamical systems , 2006 .

[3]  Akira Hirose,et al.  Generalization Characteristics of Complex-Valued Feedforward Neural Networks in Relation to Signal Coherence , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Qiankun Song,et al.  Design of controller on synchronization of chaotic neural networks with mixed time-varying delays , 2009, Neurocomputing.

[5]  Guobao Zhang,et al.  Finite-time synchronization of delayed neural networks , 2017, 2017 Chinese Automation Congress (CAC).

[6]  F. M. Kakmeni,et al.  A new adaptive observer-based synchronization scheme for private communication , 2006 .

[7]  Huaguang Zhang,et al.  Synchronization stability in complex interconnected neural networks with nonsymmetric coupling , 2013, Neurocomputing.

[8]  Xinsong Yang,et al.  Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations , 2016 .

[9]  Li Sheng,et al.  Exponential synchronization of a class of neural networks with mixed time-varying delays and impulsive effects , 2008, Neurocomputing.

[10]  K. Aihara,et al.  Chaotic neural networks , 1990 .

[11]  Xiaohui Xu,et al.  Exponential stability of complex-valued neural networks with mixed delays , 2014, Neurocomputing.

[12]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

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

[14]  Z. Tan,et al.  ASSOCIATIVE MEMORY USING SYNCHRONIZATION IN A CHAOTIC NEURAL NETWORK , 2001 .

[15]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[16]  Xiaohui Xu,et al.  Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect , 2017, Int. J. Syst. Sci..

[17]  Stefano Nolfi,et al.  Good teaching inputs do not correspond to desired responses in ecological neural networks , 1994, Neural Processing Letters.

[18]  Bo Zhou,et al.  Boundedness and complete stability of complex-valued neural networks with time delay. , 2013, IEEE transactions on neural networks and learning systems.

[19]  Jacek M. Zurada,et al.  Discrete-Time Recurrent Neural Networks With Complex-Valued Linear Threshold Neurons , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Danilo P. Mandic,et al.  Class of Widely Linear Complex Kalman Filters , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[22]  Fei Yang,et al.  Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control , 2016 .

[23]  Chuandong Li,et al.  Finite-time lag synchronization of delayed neural networks , 2014, Neurocomputing.

[24]  Xiaohong Wang,et al.  Finite-time synchronization of drive-response systems via periodically intermittent adaptive control , 2014, J. Frankl. Inst..

[25]  Haijun Jiang,et al.  Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control , 2014, Neurocomputing.

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

[27]  D.-L. Lee,et al.  Improvements of Complex-Valued Hopfield Associative Memory by Using Generalized Projection Rules , 2006, IEEE Transactions on Neural Networks.

[28]  Xinsong Yang,et al.  Can neural networks with arbitrary delays be finite-timely synchronized? , 2014, Neurocomputing.

[29]  Hao Shen,et al.  Finite-time H∞ synchronization for complex networks with semi-Markov jump topology , 2015, Commun. Nonlinear Sci. Numer. Simul..