Convergence of non-autonomous discrete-time Hopfield model with delays

This paper is concerned with boundedness, convergence of solution of a class of non-autonomous discrete-time delayed Hopfield neural network model. Using the inequality technique, we obtain some sufficient conditions ensuring the boundedness of solutions of the discrete-time delayed Hopfield models in time-varying situation. Then, by exploring intrinsic features between non-autonomous system and its asymptotic equations, several novel sufficient conditions are established to ensure that all solutions of the networks converge to the solution of its asymptotic equations. Especially, for case of asymptotic autonomous system or asymptotic periodic system, we obtain some sufficient conditions ensuring all solutions of original system convergent to equilibrium or periodic solution of asymptotic system, respectively. An example is provided for demonstrating the effectiveness of the global stability conditions presented. Our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria.

[1]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[2]  Jun Wang,et al.  A recurrent neural network for solving linear projection equations , 2000, Neural Networks.

[3]  Eugenius Kaszkurewicz,et al.  Existence and stability of a unique equilibrium in continuous-valued discrete-time asynchronous Hopfield neural networks , 1996, IEEE Trans. Neural Networks.

[4]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous cellular neural networks with delay , 2003 .

[5]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

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

[7]  Dewen Hu,et al.  Stability and bifurcation analysis on a discrete-time neural network , 2005 .

[8]  Zidong Wang,et al.  Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis , 2007 .

[9]  Jinde Cao,et al.  Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays , 2003 .

[10]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[11]  Leon O. Chua,et al.  An extended class of synaptic operators with application for efficient VLSI implementation of cellular neural networks , 1998 .

[12]  Jinde Cao,et al.  A delayed neural network for solving linear projection equations and its analysis , 2005, IEEE Transactions on Neural Networks.

[13]  Zidong Wang,et al.  A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays , 2007 .

[14]  Zhigang Zeng,et al.  Multiperiodicity of Discrete-Time Delayed Neural Networks Evoked by Periodic External Inputs , 2006, IEEE Transactions on Neural Networks.

[15]  Nikita Barabanov,et al.  Stability analysis of discrete-time recurrent neural networks , 2002, IEEE Trans. Neural Networks.

[16]  R. Palmer,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[17]  S. Arik.  Stability analysis of delayed neural networks , 2000 .

[18]  Toru Kumagai,et al.  Learning of limit cycles in discrete-time neural network , 1996, Neurocomputing.

[19]  Zidong Wang,et al.  Global Synchronization Control of General Delayed Discrete-Time Networks With Stochastic Coupling and Disturbances , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Jinde Cao,et al.  Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses , 2008, J. Frankl. Inst..

[21]  Zhaohui Yuan,et al.  Convergence of Nonautonomous Cohen–Grossberg-Type Neural Networks With Variable Delays , 2008, IEEE Transactions on Neural Networks.

[22]  Zhaohui Yuan,et al.  On the Global asymptotic Stability Analysis of Delayed Neural Networks , 2005, Int. J. Bifurc. Chaos.

[23]  J. Si,et al.  Analysis and synthesis of a class of discrete-time neural networks with nonlinear interconnections , 1994 .

[24]  Jun Wang,et al.  Global stability of a class of discrete-time recurrent neural networks , 2002 .

[25]  Qiankun Song,et al.  Passivity analysis of discrete-time stochastic neural networks with time-varying delays , 2009, Neurocomputing.

[26]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

[27]  Liang Jin,et al.  Globally asymptotical stability of discrete-time analog neural networks , 1996, IEEE Trans. Neural Networks.

[28]  Zhang Yi,et al.  Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions , 2004, IEEE Transactions on Neural Networks.

[29]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Xiaofeng Liao,et al.  Global exponential stability for a class of retarded functional differential equations with applications in neural networks , 2004 .

[31]  Yongkun Li.  Global stability and existence of periodic solutions of discrete delayed cellular neural networks , 2004 .

[32]  K. Aihara,et al.  Chaos and asymptotical stability in discrete-time neural networks , 1997, chao-dyn/9701020.

[33]  Corneliu A. Marinov,et al.  Stable computational dynamics for a class of circuits with O(N) interconnections capable of KWTA and rank extractions , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  A. N. Michel,et al.  Robustness analysis of a class of discrete-time recurrent neural networks under perturbations , 1999 .

[35]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[36]  Lihong Huang,et al.  Periodic oscillation for discrete-time Hopfield neural networks , 2004 .