电磁感应下分数阶神经元网络的斑图动力学分析及控制

The dynamic characteristic of neuron network is one of the frontier topics in the field of computational neuroscience at present. The change of electromagnetic field flux of nervous system or its medium caused by external electromagnetic radiation could trigger the migration of neuron population discharge modes，while neuron population abnormal discharge will induce a variety of neurological diseases. Therefore, precisely depicting the abnormal discharge of the nervous system is one of the difficulties in current computational neurosciences. In this project, according to the property that fractional-order system can accurately simulate delay effects, via nonlinear analysis method, following research work about fractional-order neuron systems and the network composed of them under electromagnetic induction is to be carried out, (1) The effect of inductor loop current on the stability, existence and uniqueness of solutions, bifurcation, chaos together with other dynamics of fractional-order neurons and the networks composed of them; (2)The effect of time-delay, impulse, different network topologies on the spatiotemporal pattern of fractional-order neural network under electromagnetic induction and the inducing mechanism; (3)The effect of time-delay, impulse, order as well as other factors on the synchronization effect and synchronization area of fractional-order neural networks under electromagnetic induction, along with the stability of synchronization pattern of fractional-order neural network under electromagnetic induction and the influence factors of stability. The research results of this project not only can provide theoretical basis for the application of fractional-order neural network, but also are of great significance for understanding the mechanism of neural information transmission and coding under electromagnetic radiation.

神经元网络的动态特性是当前计算神经科学领域的前沿课题之一。外界电磁辐射引起的神经系统或介质的电磁场通量的变化会引发神经元群体放电模式的迁移，神经元群体异常放电会诱发各种神经性疾病，精确刻画神经系统的异常放电现象是目前计算神经科学的难点之一。本项目拟利用分数阶系统能够精确模拟时滞效果的特性，借助非线性分析方法，对电磁感应下分数阶神经元系统及其网络开展如下研究工作：(1)电感回路电流对分数阶神经元及其网络的稳定性、解的存在唯一性、分岔、混沌等动力学行为的影响；(2)时滞、脉冲、网络的不同拓扑结构对电磁感应下分数阶神经元网络时空斑图的影响及诱发机制；(3)时滞、脉冲、阶次等对电磁感应下分数阶神经元网络同步效应及同步化区域的影响，电磁感应下分数阶神经元网络同步斑图的稳定性及其影响因素。项目的研究成果可为分数阶神经元网络的应用提供理论依据，对理解电磁辐射下神经信息传递和编码的作用机制具有重要意义。

神经元网络的动态特性是当前计算神经科学领域的前沿课题之一。外界电磁辐射引起的神经系统或介质的电磁场通量的变化会引发神经元群体放电模式的迁移，神经元群体异常放电会诱发多种神经性疾病。为精确刻画神经系统的异常放电现象，本项目利用分数阶系统能够精确模拟时滞效果的特性，借助非线性分析方法，揭示了电感回路电流对分数阶神经元及其网络的稳定性、解的存在唯一性、分岔、混沌等动力学行为的影响；给出了时滞、脉冲、网络的不同拓扑结构对电磁感应下分数阶神经元网络时空斑图的影响及诱发机制；说明时滞、脉冲、阶次等对电磁感应下分数阶神经元网络同步效应及同步化区域具有一定的影响，分析了电磁感应下分数阶神经元网络同步斑图的稳定性及其影响因素。项目研究成果可为分数阶神经元网络的应用提供理论依据，对理解电磁辐射下神经信息传递和编码的作用机制具有重要意义。