瞬时混沌神经网络的混沌动力学

基金项目: 国家自然科学基金资助项目(70271065)

Chaos in Transiently Chaotic Neural Networks

Department of Mathematics, Research Center for Nonlinear Science and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, P. R. China

摘要: 首先利用"不可分意味着混沌"从理论上证明了一维瞬时混沌神经网络在一定的条件下按Li-Yorke意义是混沌的;特别地,进一步推出了混沌神经网络按Li-Yorke意义是混沌的充分条件,而这将从理论上证明Aihara等人通过数值计算所得结论;最后,为说明前面的结论给出了一个例子及其数值计算的结果。
- 混沌神经网络 /
- 混沌 /
- 不可分性
Abstract: It was theoretically proved that one-dimensional transiently chaotic neural networks have chaotic structure in sense of Li-Yorke theorem with some given assumptions using that no division implies chaos.In particular,it is further derived sufficient conditions for the existence of chaos in sense of Li-Yorke theorem in chaotic neural network,which leads to the fact that Aihara has demonstrated by numerical method.Finally,an example and numerical simulation are shown to illustrate and reinforce the previous theory.
- chaotic neural networks /
- chaos /
- no division

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