Dynamics of complex-valued neural networks with variable coefficients and proportional delays

Abstract In this paper, the dynamics including boundedness and stability for a general class of complex-valued neural networks with variable coefficients and proportional delays are investigated. By employing inequality techniques and mathematical analysis method, some sufficient criteria to guarantee boundedness and global exponential stability are established for the considered neural networks. As a special case that the coefficients of networks are constants, sufficient criteria are also derived to guarantee the existence, uniqueness and global exponential stability of the equilibrium point. This work generalizes and improves previously known results, and the obtained criteria can be tested and applied easily in practice. An illustrative example demonstrates the feasibility of the proposed results.

[1]  Liqun Zhou,et al.  Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays , 2012, Neural Processing Letters.

[2]  Jun Hu,et al.  A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements , 2016, Autom..

[3]  Bing Chen,et al.  Global Stability Criterion for Delayed Complex-Valued Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Fuad E. Alsaadi,et al.  Robust ${\mathscr {H}}_{\infty }$ Filtering for a Class of Two-Dimensional Uncertain Fuzzy Systems With Randomly Occurring Mixed Delays , 2017, IEEE Transactions on Fuzzy Systems.

[5]  Eva Kaslik,et al.  Multistability in impulsive hybrid Hopfield neural networks with distributed delays , 2011 .

[6]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[7]  Qiankun Song,et al.  Boundedness and Complete Stability of Complex-Valued Neural Networks With Time Delay , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Derui Ding,et al.  Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks , 2017, Autom..

[9]  Lei Guo,et al.  Optimal control for networked control systems with disturbances: a delta operator approach , 2017 .

[10]  Jinde Cao,et al.  Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays , 2015, Neural Networks.

[11]  Jinde Cao,et al.  Matrix measure based stability criteria for high-order neural networks with proportional delay , 2015, Neurocomputing.

[12]  Zhenjiang Zhao,et al.  Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays , 2015, Neurocomputing.

[13]  Ivanka M. Stamova,et al.  Global exponential stability for impulsive cellular neural networks with time-varying delays , 2008 .

[14]  Fuad E. Alsaadi,et al.  Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays , 2017, Neurocomputing.

[15]  Qiankun Song,et al.  Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales , 2013, Neurocomputing.

[16]  Pagavathigounder Balasubramaniam,et al.  Existence and Global Asymptotic Stability of Fuzzy Cellular Neural Networks with Time Delay in the Leakage Term and Unbounded Distributed Delays , 2011, Circuits Syst. Signal Process..

[17]  Liqun Zhou Global asymptotic stability of cellular neural networks with proportional delays , 2014 .

[18]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.

[19]  Jun Hu,et al.  Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements , 2013, Int. J. Control.

[20]  Tianping Chen,et al.  Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[22]  Jinde Cao,et al.  Further analysis of global μ-stability of complex-valued neural networks with unbounded time-varying delays , 2015, Neural Networks.

[23]  Tingwen Huang,et al.  An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities , 2016, IEEE Transactions on Cybernetics.

[24]  Zhenjiang Zhao,et al.  Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects , 2016, Neural Networks.

[25]  K. Gopalsamy,et al.  Exponential stability of artificial neural networks with distributed delays and large impulses , 2008 .

[26]  Jinde Cao,et al.  Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays , 2006 .

[27]  Lei Guo,et al.  Composite control of linear quadratic games in delta domain with disturbance observers , 2017, J. Frankl. Inst..

[28]  Fuad E. Alsaadi,et al.  $H_\infty $ Control for 2-D Fuzzy Systems With Interval Time-Varying Delays and Missing Measurements , 2017, IEEE Transactions on Cybernetics.

[29]  Donq-Liang Lee,et al.  Relaxation of the stability condition of the complex-valued neural networks , 2001, IEEE Trans. Neural Networks.

[30]  Ruya Samli,et al.  Global robust stability analysis of uncertain neural networks with time varying delays , 2015, Neurocomputing.

[31]  Parameswaran Ramanathan,et al.  Proportional differentiated services: delay differentiation and packet scheduling , 2002, TNET.

[32]  Jitao Sun,et al.  Further Investigate the Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2014 .

[33]  Zhenjiang Zhao,et al.  Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays , 2016, Neural Networks.

[34]  Bingwen Liu,et al.  Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays , 2016, Neurocomputing.

[35]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

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

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

[38]  Daniel W. C. Ho,et al.  Observer-Based Event-Triggering Consensus Control for Multiagent Systems With Lossy Sensors and Cyber-Attacks , 2017, IEEE Transactions on Cybernetics.

[39]  Zidong Wang,et al.  Event-based security control for discrete-time stochastic systems , 2016 .

[40]  Yixian Yang,et al.  Asymptotic stability of cellular neural networks with multiple proportional delays , 2014, Appl. Math. Comput..

[41]  John Ockendon,et al.  The dynamics of a current collection system for an electric locomotive , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.