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 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.展开更多
Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previo...Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.展开更多
基金the National Natural Science Foundation of China (70271065)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.11071238)the Key Lab of Random Complex Structures and Data Science,CAS(No.2008DP173182)the National Center for Mathematics and Interdisciplinary Sciences,CAS(No.Y029184K51)
文摘Under the condition that the damping factor is between zero and one, chaotic dynamics is proved to exist in one-dimensional transiently chaotic neural networks by Li-Misiurewicz theorem. This result extends the previous result which is done under the condition that the damping factor is zero. Because the value of damping factor affects the speed of dynamical process of transiently chaotic neural networks, this result provides more complete theoretical basis for applications. Finally, two examples by numerical simulation are given to reinforce and illustrate this result.
