Output convergence analysis for a class of delayed recurrent neural networks with time-varying inputs

This paper studies the output convergence of a class of recurrent neural networks with time-varying inputs. The model of the studied neural networks has different dynamic structure from that in the well known Hopfield model, it does not contain linear terms. Since different structures of differential equations usually result in quite different dynamic behaviors, the convergence of this model is quite different from that of Hopfield model. This class of neural networks has been found many successful applications in solving some optimization problems. Some sufficient conditions to guarantee output convergence of the networks are derived.

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

[2]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

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

[4]  Tamás Roska,et al.  Image compression by cellular neural networks , 1998 .

[5]  Zhang Yi,et al.  Estimate of exponential convergence rate and exponential stability for neural networks , 1999, IEEE Trans. Neural Networks.

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

[7]  Jun Wang,et al.  Global exponential stability of continuous-time interval neural networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Jun Wang,et al.  Global dissipativity of continuous-time recurrent neural networks with time delay. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[10]  Jun Wang,et al.  Global output convergence of a class of continuous-time recurrent neural networks with time-varying thresholds , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Jun Wang.  Analysis and design of an analog sorting network , 1995, IEEE Trans. Neural Networks.

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

[13]  H Lu.  Stability criteria for delayed neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Jun Wang.  Analogue neural network for solving the assignment problem , 1992 .

[15]  Jun Wang,et al.  Primal and dual assignment networks , 1997, IEEE Trans. Neural Networks.

[16]  Jianhong Wu,et al.  A new method of Lyapunov functionals for delayed cellular neural networks , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[17]  Jun Wang.  Analysis and design of a recurrent neural network for linear programming , 1993 .

[18]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[19]  Khashayar Pakdaman,et al.  Transient regime duration in continuous-time neural networks with delay , 1998 .

[20]  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.

[21]  Zhang Yi,et al.  Erratum: Dynamical stability conditions for Lotka-Volterra recurrent neural networks with delays [Phys. Rev. E 66 , 011910 (2002)] , 2002 .

[22]  Shun-ichi Amari,et al.  Exponential Convergence of Delayed Dynamical Systems , 2001, Neural Computation.

[23]  Jun Wang.  A recurrent neural network for solving the shortest path problem , 1996 .

[24]  Xue-Bin Liang,et al.  Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem , 2001, IEEE Trans. Neural Networks.

[25]  Tamás Roska,et al.  Image compression by cellular neural networks , 1998 .

[26]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[27]  Wang,et al.  Global stability and local stability of Hopfield neural networks with delays. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Zhang Yi,et al.  Global exponential convergence of recurrent neural networks with variable delays , 2004, Theor. Comput. Sci..

[29]  L. Pandolfi,et al.  On stability of cellular neural networks with delay , 1993 .

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

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

[32]  M. Forti.  On Global Asymptotic Stability of a Class of Nonlinear Systems Arising in Neural Network Theory , 1994 .

[33]  Jinde Cao,et al.  Novel Stability Criteria for Delayed Cellular Neural Networks , 2003, Int. J. Neural Syst..