Robust Global Exponential Stability for Interval Reaction–Diffusion Hopfield Neural Networks With Distributed Delays

This brief presents a sufficient condition for the existence, uniqueness, and robust global exponential stability of the equilibrium solution for a class of interval reaction diffusion Hopfield neural networks with distributed delays and Dirichlet boundary conditions by constructing suitable Lyapunov functional and utilizing some inequality techniques. The result imposes constraint conditions on the boundary values of the network parameters. The result is also easy to verify and plays an important role in the design and application of globally exponentially stable neural circuits.

[1]  Kwong-Sak Leung,et al.  Convergence analysis of cellular neural networks with unbounded delay , 2001 .

[2]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[3]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .

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

[5]  Anthony W. Leung,et al.  Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering , 1989 .

[6]  Linshan Wang,et al.  Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays , 2006 .

[7]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[8]  H. Ye,et al.  Robust stability of nonlinear time-delay systems with applications to neural networks , 1996 .

[9]  Anthony W. Leung,et al.  Systems of Nonlinear Partial Differential Equations , 1989 .

[10]  Karl Kunisch,et al.  Distributed Parameter Systems , 1985 .

[11]  Vedat Tavsanoglu,et al.  On the global robust stability of delayed neural networks , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[12]  Marco Gilli,et al.  Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions , 1994 .

[13]  Viorel Barbu,et al.  Distributed Parameter Systems , 1992, Concise Encyclopedia of Modelling & Simulation.

[14]  Mark P. Joy,et al.  Results concerning the absolute stability of delayed neural networks , 2000, Neural Networks.

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

[16]  Hongyong Zhao,et al.  Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays [rapid communication] , 2005 .

[17]  Jianhua Sun,et al.  Convergence Dynamics of Stochastic Reaction-diffusion Recurrent Neural Networks with Delays , 2005, Int. J. Bifurc. Chaos.

[18]  Qiang Zhang,et al.  Global exponential stability of Hopfield neural networks with continuously distributed delays , 2003 .

[19]  Junguo Lu Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[20]  Yoshihiro Suda,et al.  Absolutely exponential stability of a class of neural networks with unbounded delay , 2004, Neural Networks.

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

[22]  Anthony W. Leung,et al.  Equilibria and stabilities for competing-species reaction-diffusion equations with Dirichlet boundary data , 1980 .

[23]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

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

[26]  Teh-Lu Liao,et al.  Global stability for cellular neural networks with time delay , 2000, IEEE Trans. Neural Networks Learn. Syst..

[27]  Alberto Tesei,et al.  Competition systems with Dirichlet boundary conditions , 1982 .