In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chao...In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results.展开更多
Synchronization and coherence of chaotic Morris-Lecar （ML） neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, e...Synchronization and coherence of chaotic Morris-Lecar （ML） neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, even though all neurons are chaotic when uncoupled. Moreover, the coherence of the neurons exhibits a non-monotonic dependence on the density of shortcuts. There is an optimal number of shortcuts at which the neurons＇ motion is most ordered, i.e. the order parameter （the characteristic correlation time） that is introduced to measure the coherence of the neurons has a maximum. These phenomena imply that stochastic shortcuts can tame spatiotemporal chaos. The effects of the coupling strength have also been studied. The value of the optimal number of shortcuts goes down as the coupling strength increases.展开更多
基金supported by the Beijing Natural Science Foundation,China(Grant No.4132005)the National Natural Science Foundation of China(Grant No.61403006)+1 种基金the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions,China(Grant No.YETP1449)the Project of Scientific and Technological Innovation Platform,China(Grant No.PXM2015 014213 000063)
文摘In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results.
基金Project supported by the National Natural Science Foundation of China （Grant No 20433050）, the Program for New Century Excellent Talents in University, the Fok Ying Dong Education Foundation and the Foundation for the Author of National ,Excellent Doctoral Dissertation of China.
文摘Synchronization and coherence of chaotic Morris-Lecar （ML） neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, even though all neurons are chaotic when uncoupled. Moreover, the coherence of the neurons exhibits a non-monotonic dependence on the density of shortcuts. There is an optimal number of shortcuts at which the neurons＇ motion is most ordered, i.e. the order parameter （the characteristic correlation time） that is introduced to measure the coherence of the neurons has a maximum. These phenomena imply that stochastic shortcuts can tame spatiotemporal chaos. The effects of the coupling strength have also been studied. The value of the optimal number of shortcuts goes down as the coupling strength increases.
