Stability in impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays: A general analysis

In this paper, we investigate a class of impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays. By establishing the delay differential inequality with impulsive initial conditions, and employing the homeomorphism theory, the M-matrix theory and the inequality [email protected]?"k"="1^lb"k^q^"^[email protected]?(1/r)(a^[email protected]?"k"="1^lq"kb"k^r) (a>=0,b"k>=0,q"k>=0 with @?"k"="1^lq"k=r-1, and r>=1), some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen-Grossberg-type BAM neural networks with time-varying delays are derived. In particular, the estimate of the exponential convergence rate which depends on the system parameters and the impulsive disturbance intension is also provided. An example is given to show the effectiveness of the results obtained here.

[1]  Chaolong Zhang,et al.  Global stability analysis of impulsive BAM type Cohen-Grossberg neural networks with delays , 2007, Appl. Math. Comput..

[2]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[3]  Zhenkun Huang,et al.  Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses , 2008 .

[4]  Li Wan,et al.  Impulsive effects on stability of Cohen–Grossberg-type bidirectional associative memory neural networks with delays , 2009 .

[5]  Daoyi Xu,et al.  Impulsive delay differential inequality and stability of neural networks , 2005 .

[6]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[7]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[8]  Jinde Cao,et al.  Exponential stability of periodic solution to Cohen-Grossberg-type BAM networks with time-varying delays , 2009, Neurocomputing.

[9]  Yongkun Li.  Global exponential stability of BAM neural networks with delays and impulses , 2005 .

[10]  Réjean Plamondon,et al.  Stability analysis of bidirectional associative memory networks with time delays , 2003, IEEE Trans. Neural Networks.

[11]  Zhenkun Huang,et al.  Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses , 2008 .

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

[13]  Jitao Sun,et al.  Stability analysis of delayed Cohen–Grossberg BAM neural networks with impulses via nonsmooth analysis☆ , 2009 .

[14]  Min Huang,et al.  Global asymptotic stability of delay bam neural networks with impulses based on matrix theory , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[15]  Zhenkun Huang,et al.  Existence and globally exponential stability of equilibrium for BAM neural networks with impulses , 2008 .

[16]  B. Cui,et al.  Impulsive effects on global asymptotic stability of delay BAM neural networks , 2008 .

[17]  R. Jackson.  Inequalities , 2007, Algebra for Parents.

[18]  Xiaodi Li,et al.  Exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control , 2009, Neurocomputing.

[19]  Kelin Li,et al.  Delay-dependent stability analysis for impulsive BAM neural networks with time-varying delays , 2008, Comput. Math. Appl..

[20]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

[21]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[22]  Jinde Cao,et al.  BAM-type Cohen-Grossberg neural networks with time delays , 2008, Math. Comput. Model..

[23]  Sannay Mohamad,et al.  A unified treatment for stability preservation in computer simulations of impulsive BAM networks , 2008, Comput. Math. Appl..

[24]  Daoyi Xu,et al.  Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays , 2006, Appl. Math. Comput..

[25]  Jitao Sun,et al.  Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis , 2008, Neurocomputing.

[26]  Kondalsamy Gopalsamy,et al.  Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses , 2009 .

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

[28]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

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

[30]  Chuanzhi Bai,et al.  Stability analysis of Cohen–Grossberg BAM neural networks with delays and impulses , 2008 .

[31]  Yongkun Li,et al.  Existence and globally exponential stability of almost periodic solution for Cohen–Grossberg BAM neural networks with variable coefficients , 2009 .

[32]  Jinde Cao,et al.  Periodic bi-directional Cohen–Grossberg neural networks with distributed delays , 2007 .