论文信息 - Rich Dynamics in a Small Neural Network

Rich Dynamics in a Small Neural Network

This paper shows that rich dynamics can take place in a simple three dimensional continuous-time Hopfield neural network with its connection matrix satisfying Dale's rule. In order to get a detailed picture of the complex dynamics, chaos and transient chaos are also studied by virtue of topological horseshoe theory.

Qingdu Li | Hai Cao

[1] A. Das,et al. Chaos in a Three-Dimensional General Model of Neural Network , 2002, Int. J. Bifurc. Chaos.

[2] Xiao-Song Yang,et al. Existence of Horseshoe in a Foodweb Model , 2004, Int. J. Bifurc. Chaos.

[3] Yong Yao,et al. Model of biological pattern recognition with spatially chaotic dynamics , 1990, Neural Networks.

[4] Xiao-Song Yang,et al. Horseshoes in piecewise continuous maps , 2004 .

[5] J. E. Skinner,et al. Chaos and physiology: deterministic chaos in excitable cell assemblies. , 1994, Physiological reviews.

[6] Hugues Bersini,et al. The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks , 2002, Neural Networks.

[7] Carlos Lourenço,et al. Brain Chaos and Computation , 1996, Int. J. Neural Syst..

[8] Xiao-Song Yang,et al. Hyperchaos in Hopfield-type neural networks , 2005, Neurocomputing.

[9] Alvin Shrier,et al. Chaos in neurobiology , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[10] Leon Glass,et al. Nonlinear Dynamics and Symbolic Dynamics of Neural Networks , 1992, Neural Computation.

[11] F. Pasemann. Complex dynamics and the structure of small neural networks , 2002, Network.

[12] Hugues Bersini. The frustrated and compositional nature of chaos in small Hopfield networks , 1998, Neural Networks.

[13] D. Ruelle,et al. Ergodic theory of chaos and strange attractors , 1985 .