Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation

In addition to giving some delay-independent conditions for global stability of the bidirectional associative memory neural networks with delays, we perform analysis of local stability and Hopf bifurcation. We also work out an algorithm for determining the direction and stability of the bifurcated periodic solutions.

[1]  K. Cooke,et al.  On zeroes of some transcendental equations , 1986 .

[2]  L. Shampine,et al.  Solving DDEs in MATLAB , 2001 .

[3]  S. Ruan,et al.  Stability and bifurcation in a neural network model with two delays , 1999 .

[4]  Hongtao Lu,et al.  On stability of nonlinear continuous-time neural networks with delays , 2000, Neural Networks.

[5]  Yi Qin,et al.  On equilibria, stability, and instability of Hopfield neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

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

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

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

[9]  Junjie Wei,et al.  Qualitative analysis of a neural network model with multiple time delays , 1999 .

[10]  Réjean Plamondon,et al.  On the stability analysis of delayed neural networks systems , 2001, Neural Networks.

[11]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[12]  Bart Kosko,et al.  Unsupervised learning in noise , 1990, International 1989 Joint Conference on Neural Networks.

[13]  Kiyotoshi Matsuoka,et al.  Stability conditions for nonlinear continuous neural networks with asymmetric connection weights , 1992, Neural Networks.

[14]  K. Deimling Nonlinear functional analysis , 1985 .

[15]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[16]  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.

[17]  Jianhong Wu SYMMETRIC FUNCTIONAL DIFFERENTIAL EQUATIONS AND NEURAL NETWORKS WITH MEMORY , 1998 .

[18]  N. D. Kazarinoff,et al.  Hopf Bifurcation and Stability of Periodic Solutions of Differential-difference and Integro-differential Equations , 1978 .

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

[20]  Xingfu Zou,et al.  Patterns of sustained oscillations in neural networks with delayed interactions , 1995 .

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

[22]  M. Fiedler Special matrices and their applications in numerical mathematics , 1986 .

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

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

[25]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

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

[27]  Sue Ann Campbell,et al.  Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays , 2000, SIAM J. Appl. Math..

[28]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[29]  Q. Henry Wu,et al.  A note on stability of analog neural networks with time delays , 1996, IEEE Trans. Neural Networks.