Stability of Cohen-Grossberg-type Fuzzy Cellular Neural Networks with Distributed Delays and Impulses

In this paper, a generalized model of Cohen-Grossberg-type fuzzy cellular neural networks (FCNNs) with distributed delays and impulses is formulated and investigated. By employing the delay differential inequality with impulses initial conditions and the $M$-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for Cohen-Grossberg-type FCNNs with distributed delays and impulses are obtained. In particular, more precise estimate of exponential convergence rate is provided. An example are given to show the effectiveness of the obtained results.

[1]  Zhidong Teng,et al.  Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays , 2008, Neurocomputing.

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

[3]  K. Gopalsamy,et al.  Stability of artificial neural networks with impulses , 2004, Appl. Math. Comput..

[4]  Qianhong Zhang,et al.  Global asymptotic stability of fuzzy cellular neural networks with time-varying delays , 2008 .

[5]  Tingwen Huang Exponential stability of fuzzy cellular neural networks with distributed delay , 2006 .

[6]  Daoyi Xu,et al.  Global exponential stability of impulsive integro-differential equation , 2006 .

[7]  Leon O. Chua,et al.  Fuzzy cellular neural networks: theory , 1996, 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96).

[8]  Shitong Wang,et al.  Advanced fuzzy cellular neural network: Application to CT liver images , 2007, Artif. Intell. Medicine.

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

[10]  Wansheng Tang,et al.  Exponential stability of fuzzy cellular neural networks with constant and time-varying delays , 2004 .

[11]  Korris Fu-Lai Chung,et al.  Applying the improved fuzzy cellular neural network IFCNN to white blood cell detection , 2007, Neurocomputing.

[12]  Jinde Cao,et al.  Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays , 2006, Neurocomputing.

[13]  Tingwen Huang Exponential stability of delayed fuzzy cellular neural networks with diffusion , 2007 .

[14]  Q. Song,et al.  Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays , 2008 .

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

[16]  Kelin Li,et al.  BEHAVIOR OF IMPULSIVE FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS , 2007 .

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

[18]  Kelin Li Stability analysis for impulsive Cohen–Grossberg neural networks with time-varying delays and distributed delays , 2009 .

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

[20]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

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

[22]  K. Gopalsamy,et al.  On delay differential equations with impulses , 1989 .

[23]  Ta-lun Yang,et al.  The global stability of fuzzy cellular neural network , 1996 .

[24]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[25]  Jun-Guo Lu,et al.  Global exponential stability of fuzzy cellular neural networks with delays and reaction–diffusion terms , 2008 .

[26]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive delay differential equations , 2001 .

[27]  Ling Chen,et al.  Stability analysis of stochastic fuzzy cellular neural networks with delays , 2008, Neurocomputing.