耦合混沌Hindmarsh-Rose神经元系统中相互作用诱导的周期解研究

Research On Periodic Solution Induced By Interaction In Coupled Chaotic Hindmarsh-Rose Neurons

神经元细胞作为构成神经系统结构和功能的基本单位,在神经信号传输过程中具有非常重要的作用.采用Hindmarsh-Rose神经元模型,探究与细胞中钙离子浓度有关的一个恢复变量参数在神经元信号传递中的影响.研究表明,当改变恢复变量参数值时,单个神经元会出现周期或混沌的放电行为,并且对该参数值变化比较敏感.此外,当单个神经元为混沌放电时,随着相互作用强度的变化,耦合神经元系统不仅会出现混沌放电行为,还会产生周期放电行为,周期解窗口和混沌解窗口交替出现.当恢复变量参数值不同时,周期解窗口的个数和周期解的性质明显不同.该结论表明,该恢复变量参数在调控神经元混沌放电和周期放电行为过程中扮演着非常重要的角色.

Neurons,as the fundamental structural and functional units of nervous system,play a significant role in neural signal transmission.In this paper,we adopt HindmarshRose neuron model to explore the effect of a parameter r,which relates to the calcium ion concentration,on neuronal signal transmission.The results show that a single neuron will exhibit periodic or chaotic behavior with the varies of the values of parameter r.What’s more,two coupled chaotic neurons can exhibit periodic behavior with appropriate calcium ion concentration.With the change of the coupling strength,the periodic windows and chaotic windows will appear alternately.Especially,for different values of the parameter,the number of periodic windows will be varied,as well as the physical characteristics of the periodic solutions in the windows.These results indicate that the calcium ion concentration plays a very important role in regulating the dynamical behavior of neurons.