ISNN 2010: Advances in Neural Networks - ISNN 2010 pp 493-503 | Cite as
Stability and Hopf Bifurcation of a BAM Neural Network with Delayed Self-feedback
Conference paper
Abstract
In this paper, we consider a bidirectional associate memory(BAM) neural networks with delayed self-feedback. Regarding the self-connection delay as the bifurcation parameter, the linear stability and Hopf bifurcation analysis are carried out. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.
Keywords
Neural network Delay Stability Hopf bifurcationPreview
Unable to display preview. Download preview PDF.
References
- 1.Hopfield, J.J.: Neurons with Graded Response Have Collective Computational Properties Like Those of Two-state Neurons. J. Proc. Natl. Acad. Sci. USA 81, 3088–3092 (1984)CrossRefGoogle Scholar
- 2.Marcus, C.M., Westervelt, R.M.: Stability of Analog Neural Network with Delay. J. Phys. Rev. A 39, 347–359 (1989)CrossRefMathSciNetGoogle Scholar
- 3.Wang, L., Zou, X.: Hopf Bifurcation in Bidirectional Associative Memory Neural Networks with Delays: Analysis and Computation. J. Comput. Appl. Math. 167, 73–90 (2004)MATHCrossRefMathSciNetGoogle Scholar
- 4.Song, Y., Han, M., Wei, J.: Stability and Hopf Bifurcation on a Simplified BAM Neural Network with Delays. J. Physics D 200, 185–204 (2005)MATHCrossRefMathSciNetGoogle Scholar
- 5.Driessche, V.D., Wu, P.: Stabilization Role of Inhibitory Self-connections in a Delayed Neural Network. J. Physics D 150, 84–90 (2001)MATHCrossRefGoogle Scholar
- 6.Wang, L.: Stabilizing Hopfield Neural Networks via Inhibitory Self-connections. J. Math. Anal. Appl. 292, 135–147 (2004)MATHCrossRefMathSciNetGoogle Scholar
- 7.Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge (1981)MATHGoogle Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2010