Global exponential stability of nonautonomous neural network models with continuous distributed delays

For a family of non-autonomous differential equations with distributed delays, we give sufficient conditions for the global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Hopfield type, with time-varying coefficients and distributed delays. For these models, we establish sufficient conditions for their global exponential stability. The existence and global exponential stability of a periodic solution is also addressed. A comparison of results shows that these results are general, news, and add something new to some earlier publications.

[1]  Jianhong Wu,et al.  Introduction to Neural Dynamics and Signal Transmission Delay , 2001 .

[2]  Qiang Zhang,et al.  Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays☆ , 2008 .

[3]  J. Bélair.  Stability in a model of a delayed neural network , 1993 .

[4]  José J. Oliveira,et al.  Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks , 2008 .

[5]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[6]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[7]  Qiang Zhang,et al.  Exponential stability for nonautonomous neural networks with variable delays , 2009 .

[8]  R. Wu.  Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays , 2010 .

[9]  M. Tan,et al.  Global exponential stability of periodic solution of neural network with variable coefficients and time-varying delays , 2009 .

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

[11]  José J. Oliveira.  Global asymptotic stability for neural network models with distributed delays , 2009, Math. Comput. Model..

[12]  Zhidong Teng,et al.  Boundedness and stability for nonautonomous cellular neural networks with delay , 2003 .

[13]  R. A. Silverman,et al.  Introductory Real Analysis , 1972 .

[14]  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.

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

[16]  Jinde Cao,et al.  Dynamics of Cohen–Grossberg neural networks with time-varying delays☆ , 2006 .

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

[18]  Zhang Ji.  Global Stability of Delayed Hopfield Neural Network Models , 2001 .

[19]  Lihong Huang,et al.  Dynamics of a class of Cohen–Grossberg neural networks with time-varying delays , 2007 .

[20]  Jianhong Wu,et al.  Introduction to Functional Differential Equations , 2013 .

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

[22]  José J. Oliveira.  Global stability of a Cohen–Grossberg neural network with both time-varying and continuous distributed delays , 2011 .

[23]  José J. Oliveira,et al.  Boundedness and global exponential stability for delayed differential equations with applications , 2009, Appl. Math. Comput..