Exponential stability of reaction-diffusion generalized Cohen-Grossberg neural networks with both variable and distributed delays

In this paper, a generalized reaction-diffusion model of Cohen Grossberg neural networks with time-varying and distributed delays is investigated. By employing analytic methods, inequality technique and M -matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for Cohen-Grossberg neural networks with time-varying and distributed delays are obtained. Several examples are given to show the effectiveness of the obtained results. Mathematics Subject Classification: 92B20, 34K20

[1]  Jinde Cao,et al.  An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Chuandong Li,et al.  Global attractivity of Cohen-Grossberg model with finite and infinite delays , 2006 .

[3]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[4]  Jinde Cao,et al.  Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms , 2005 .

[5]  Zhenjiang Zhao,et al.  Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays , 2006, Comput. Math. Appl..

[6]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

[7]  邓飞其,et al.  “Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurons’’的注记 , 2005 .

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

[9]  Yi Shen,et al.  Boundedness and global exponential stability for generalized Cohen-Grossberg neural networks with variable delay , 2006, Appl. Math. Comput..

[10]  Tan Xiao.  Global Exponential Stability of Hopfield Neural Networks , 2005 .

[11]  Qiankun Song,et al.  Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms , 2006, J. Frankl. Inst..

[12]  Walter Allegretto,et al.  Stability for delayed reaction–diffusion neural networks , 2007 .

[13]  Jianhua Sun,et al.  Global asymptotic stability of Cohen–Grossberg neural network with continuously distributed delays , 2005 .

[14]  Hongyong Zhao,et al.  Global asymptotic stability of Hopfield neural network involving distributed delays , 2004, Neural Networks.

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

[16]  Kunlun Wang,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms , 2006, Neurocomputing.

[17]  Jinde Cao,et al.  Periodic solutions and exponential stability in delayed cellular neural networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Q. Song,et al.  Global exponential stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2005 .

[19]  S. Arik,et al.  Global stability analysis of Cohen–Grossberg neural networks with time varying delays , 2005 .

[20]  Zhanshan Wang,et al.  Global Asymptotic Stability of Delayed Cellular Neural Networks , 2007, IEEE Transactions on Neural Networks.

[21]  Jiye Zhang,et al.  Global exponential stability of Cohen–Grossberg neural networks with variable delays☆ , 2005 .

[22]  Kwok-Wo Wong,et al.  Criteria for exponential stability of Cohen-Grossberg neural networks , 2004, Neural Networks.

[23]  Jinde Cao,et al.  Dynamics of bidirectional associative memory networks with distributed delays and reaction–diffusion terms , 2007 .

[24]  Jinde Cao,et al.  Global exponential stability of Hopfield neural networks , 2001, Int. J. Syst. Sci..

[25]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[26]  Jianhua Sun,et al.  Exponential stability of reaction–diffusion generalized Cohen–Grossberg neural networks with time-varying delays , 2007 .

[27]  Lin Wang,et al.  Stability of Cohen-Grossberg neural networks with distributed delays , 2005, Appl. Math. Comput..

[28]  X. Lou,et al.  On global exponential stability and existence of periodic solutions for BAM neural networks with distributed delays and reaction–diffusion terms , 2008 .

[29]  Jianhua Sun,et al.  Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays , 2005 .

[30]  Jinde Cao,et al.  Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays , 2006 .

[31]  Yongkun Li.  Existence and stability of periodic solutions for Cohen–Grossberg neural networks with multiple delays , 2004 .

[32]  Xuyang Lou,et al.  Boundedness and exponential stability for nonautonomous cellular neural networks with reaction–diffusion terms , 2007 .

[33]  Jinde Cao,et al.  Global exponential stability of reaction–diffusion recurrent neural networks with time-varying delays , 2003 .

[34]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[35]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[36]  Jigen Peng,et al.  Exponential stability of Cohen¿Grossberg neural networks with a general class of activation functions , 2006 .