Stability properties for Hopfield neural networks with delays and impulsive perturbations

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new stability criteria for such system are derived by using the Lyapunov functional method and the linear matrix inequality approach. The results are related to the size of delays and impulses. Our results are less restrictive and conservative than that given in some earlier references. Finally, two numerical examples showing the effectiveness of the present criteria are given.

[1]  H. Akça,et al.  Continuous-time additive Hopfield-type neural networks with impulses , 2004 .

[2]  Qiang Zhang,et al.  Delay-dependent global stability condition for delayed Hopfield neural networks , 2007 .

[3]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[4]  Bingwen Liu,et al.  Almost periodic solutions for Hopfield neural networks with continuously distributed delays , 2007, Math. Comput. Simul..

[5]  Vimal Singh,et al.  On global robust stability of interval Hopfield neural networks with delay , 2007 .

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

[7]  Jin Zhou,et al.  Synchronization in complex delayed dynamical networks with impulsive effects , 2007 .

[8]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[9]  Xinzhi Liu,et al.  Existence and continuability of solutions for differential equations with delays and state-dependent impulses , 2002 .

[10]  Gang Wang,et al.  New criteria of global exponential stability for a class of generalized neural networks with time-varying delays , 2006, Neurocomputing.

[11]  Yang Zhi-chun,et al.  GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS , 2006 .

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

[13]  Yu Zhang,et al.  Stability of impulsive neural networks with time delays , 2005 .

[14]  Daoyi Xu,et al.  Delay-dependent stability analysis for impulsive neural networks with time varying delays , 2008, Neurocomputing.

[15]  Daoyi Xu,et al.  Stability Analysis of Delay Neural Networks With Impulsive Effects , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[16]  R. Dickson,et al.  Stability analysis of Hopfield neural networks with uncertainty , 2001 .

[17]  J. Ruan,et al.  Global stability analysis of impulsive Cohen–Grossberg neural networks with delay , 2005 .

[18]  Xilin Fu,et al.  W-stability theorems of nonlinear impulsive functional differential systems , 2008 .

[19]  Aihui Zhou,et al.  A finite element method for the Frobenius-Perron operator equation , 1999, Appl. Math. Comput..

[20]  Xinzhi Liu,et al.  Boundedness for impulsive delay differential equations and applications to population growth models , 2003 .

[21]  Xiaodi Li,et al.  Oscillation of higher order impulsive differential equations of mixed type with constant argument at fixed time , 2008, Mathematical and computer modelling.

[22]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[23]  Jinde Cao,et al.  Globally exponential stability conditions for cellular neural networks with time-varying delays , 2002, Appl. Math. Comput..

[24]  Qiang Zhang,et al.  Delay-dependent global stability results for delayed Hopfield neural networks , 2007 .

[25]  Xinzhi Liu,et al.  Uniform boundedness and stability criteria in terms of two measures for impulsive integro-differential equations , 1999, Appl. Math. Comput..

[26]  Duhamel's principle for temporally inhomogeneous evolution equations in Banach space , 1984 .

[27]  Jinde Cao,et al.  On global asymptotic stability of recurrent neural networks with time-varying delays , 2003, Appl. Math. Comput..

[28]  Hongjun Xiang,et al.  Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks , 2006 .