Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

[1]  Zengyun Wang,et al.  Global stability analysis for delayed complex-valued BAM neural networks , 2016, Neurocomputing.

[2]  Zhenjiang Zhao,et al.  Multistability of complex-valued neural networks with time-varying delays , 2017, Appl. Math. Comput..

[3]  Jinling Liang,et al.  Robust State Estimation for Delayed Complex-Valued Neural Networks , 2017, Neural Processing Letters.

[4]  Fuad E. Alsaadi,et al.  State estimation of complex-valued neural networks with two additive time-varying delays , 2018, Neurocomputing.

[5]  Song Zhu,et al.  Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays , 2017 .

[6]  Ziye Zhang,et al.  Finite-Time Stability for Delayed Complex-Valued BAM Neural Networks , 2017, Neural Processing Letters.

[7]  G. Feng,et al.  Delay-dependent stability for uncertain stochastic neural networks with time-varying delay , 2007 .

[8]  Zhenjiang Zhao,et al.  Stability analysis of complex-valued neural networks with probabilistic time-varying delays , 2015, Neurocomputing.

[9]  Zidong Wang,et al.  Exponential stability of uncertain stochastic neural networks with mixed time-delays , 2007 .

[10]  Junfeng Chen,et al.  Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays , 2015, Neurocomputing.

[11]  Ju H. Park,et al.  New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays , 2008, Appl. Math. Comput..

[12]  Rajendran Samidurai,et al.  Robust dissipativity analysis for uncertain neural networks with additive time-varying delays and general activation functions , 2019, Math. Comput. Simul..

[13]  Xuerong Mao,et al.  Stability of stochastic delay neural networks , 2001, J. Frankl. Inst..

[14]  S. Ramasamy,et al.  Dissipativity and passivity analysis for discrete‐time complex‐valued neural networks with leakage delay and probabilistic time‐varying delays , 2017 .

[15]  Jinde Cao,et al.  Stability in static delayed neural networks: A nonlinear measure approach , 2006, Neurocomputing.

[16]  R. Sriraman,et al.  Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays , 2019, J. Artif. Intell. Soft Comput. Res..

[17]  P. Muthukumar,et al.  Global asymptotic stability of complex-valued neural networks with additive time-varying delays , 2017, Cognitive Neurodynamics.

[18]  Jian Guo,et al.  Passivity Analysis of Stochastic Memristor-Based Complex-Valued Recurrent Neural Networks with Mixed Time-Varying Delays , 2017, Neural Processing Letters.

[19]  Jinde Cao,et al.  Exponential stability of complex-valued memristor-based neural networks with time-varying delays , 2017, Appl. Math. Comput..

[20]  Xiaofei Li,et al.  Mean square exponential stability of stochastic Hopfield neural networks with mixed delays , 2017 .

[21]  Jianhua Sun,et al.  Mean square exponential stability of stochastic delayed Hopfield neural networks , 2005 .

[22]  Jacek M. Zurada,et al.  Complex-valued multistate neural associative memory , 1996, IEEE Trans. Neural Networks.

[23]  Jinde Cao,et al.  Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks , 2018, Entropy.

[24]  Song Zhu,et al.  Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay , 2017, Int. J. Syst. Sci..

[25]  Jian Chen,et al.  Further stability analysis for delayed complex-valued recurrent neural networks , 2017, Neurocomputing.

[26]  Lan Wang,et al.  Robust state estimation for stochastic complex-valued neural networks with sampled-data , 2017, Neural Computing and Applications.

[27]  Ju H. Park,et al.  Stability and dissipativity analysis of static neural networks with interval time-varying delay , 2015, J. Frankl. Inst..

[28]  Ravi P. Agarwal,et al.  Stability Analysis of Cohen–Grossberg Neural Networks with Random Impulses , 2018, Mathematics.

[29]  Yasuaki Kuroe,et al.  Phase dynamics of complex-valued neural networks and its application to traffic signal control , 2005, Int. J. Neural Syst..

[30]  Xin Zhou,et al.  Delay-partitioning approach for systems with interval time-varying delay and nonlinear perturbations , 2015, J. Comput. Appl. Math..

[31]  Jinde Cao,et al.  A based-on LMI stability criterion for delayed recurrent neural networks , 2006 .

[32]  Song Zhu,et al.  Leakage delay-dependent stability analysis for complex-valued neural networks with discrete and distributed time-varying delays , 2019, Neurocomputing.

[33]  Rajendran Samidurai,et al.  New delay dependent robust asymptotic stability for uncertain stochastic recurrent neural networks with multiple time varying delays , 2012, J. Frankl. Inst..

[34]  Xinzhi Liu,et al.  Exponential stability of impulsive complex-valued neural networks with time delay , 2019, Math. Comput. Simul..

[35]  Jinde Cao,et al.  Effects of leakage delay on global asymptotic stability of complex‐valued neural networks with interval time‐varying delays via new complex‐valued Jensen's inequality , 2018, International Journal of Adaptive Control and Signal Processing.

[36]  Simon X. Yang,et al.  Robust stability criteria for uncertain stochastic neural networks of neutral-type with interval time-varying delays , 2011, Neural Computing and Applications.

[37]  R. Sriraman,et al.  Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays , 2020, Math. Comput. Simul..

[38]  Zengyun Wang,et al.  Dynamical Behavior of Complex-Valued Hopfield Neural Networks with Discontinuous Activation Functions , 2017, Neural Processing Letters.

[39]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[40]  Jinde Cao,et al.  Global Robust Synchronization of Fractional Order Complex Valued Neural Networks with Mixed Time Varying Delays and Impulses , 2019, International Journal of Control, Automation and Systems.

[41]  Song Zhu,et al.  Passivity analysis of stochastic delayed neural networks with Markovian switching , 2011, Neurocomputing.

[42]  Xiaohui Xu,et al.  Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays , 2019, Complex..

[43]  Fuad E. Alsaadi,et al.  Global lagrange stability of complex-valued neural networks of neutral type with time-varying delays , 2016, Complex..

[44]  Junwei Lu,et al.  Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays , 2018, Entropy.

[45]  Wei Xing Zheng,et al.  Stability Analysis of Time-Delay Neural Networks Subject to Stochastic Perturbations , 2013, IEEE Transactions on Cybernetics.