Bifurcation in two-dimensional neural network model with delay
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A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory.
- Chen Y, Wu J. Slowly oscillating periodic solutions for a delayed frustrated network of two neurons [J].J Math Anal Appl, 2001,259(1):188–208. CrossRef
- Wei J, Ruan S. Stability and bifurcation in a neural network model with two delays[J].Physica D, 1999,130(3/4):255–272. CrossRef
- Faria T. On a planar system modelling a neuron network with memory[J].J Differential Equations, 2000,168(1):129–149. CrossRef
- Wei J, Velarde M, Makarov V. Oscillatory phenomena and stability of periodic solutions in a simple neural network with delay[J].Nonlinear Phenomena in Complex Systems, 2002,5(4):407–417.
- Wu J. Symmetric functional differential equations and neural networks with memory[J].Trans Amer Math Soc, 1998,350(12):4799–4838. CrossRef
- Wu J.Introduction to Neural Dynamics and Signal Transmission Delay[M]. Walter de Gruyter, Berlin, New York, 2001, 120–150.
- Babcock K L, Westervelt R M. Dynamics of simple electronic neural networks[J].Physica D, 1987,28(4):305–359. CrossRef
- Hassard B D, Kazarinoff N D, Wan Y H.Theory and Applications of Hopf Bifurcation[M]. Cambridge University Press, Cambridge, 1981.
- Bifurcation in two-dimensional neural network model with delay
Applied Mathematics and Mechanics
Volume 26, Issue 2 , pp 210-217
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- neural network
- centre manifold
- pitchfork bifurcation
- Hopf bifurcation
- Industry Sectors
- Author Affiliations
- 1. Department of Mathematics, Harbin Institute of Technology, 150001, harbin, P.R. China
- 2. Key Laboratory of Forestry Plant Ecology of Ministry of Education, Northeast Forestry University, 150040, Harbin, P.R. China
- 3. Department of Basic Science and Art, Changchun Taxation College, 130022, Changchun, P.R. China