Evaluation Methods of Chaotic State in Spiking Neural System with State Dependent Jump
Evaluation Methods of Chaotic State in Spiking Neural System with State Dependent Jump
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DOI：
10.5687/iscie.29.210
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. Nobukawa;H. Nishimura;Teruya Yamanishi;Jian-Qin Liu
中科院分区：
文献类型：
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作者：
S. Nobukawa;H. Nishimura;Teruya Yamanishi;Jian-Qin Liu
Izhikevich神经元模型结合了连续发放机制和发放后的不连续重置过程，能够再现实际神经系统中包括混沌发放在内的几乎所有发放活动。当在该模型中的混沌状态进行评估时，它是已知的，传统的李雅普诺夫指数的连续轨迹的前提下，不能被应用，由于在复位过程中的状态依赖跳跃。为了计算具有复位过程的系统的李雅普诺夫指数，需要用牛顿法对轨迹进行精确的数值计算，并考虑突变矩阵。利用这种方法，在Izhikevich神经元模型中找到了几条通向混沌的途径。另一方面，本文提出了结合欧拉方法和Poincaré截面上的李雅普诺夫指数的方法，并对Izhikevich神经元模型的混沌状态进行了评估。结果表明，该方法也可以通过调整初始扰动来判断混沌状态。
Izhikevich neuron model, which combines continuous spike-generation mechanisms and discontinuous resetting process after spiking, can reproduce almost all spiking activities including chaotic spiking in actual neural systems. When the chaotic state is evaluated in this model, it is known that conventional Lyapunov exponent where the continuous trajectory is presupposed cannot be applied due to the state dependent jump in the resetting process. To evaluate Lyapunov exponent in the system with the resetting process, the accurate numerical calculation for the trajectory by Newton method and the consideration for saltation matrix are needed. By virtue of this method, several routes to chaos have been found in Izhikevich neuron model. While on the other hand, in this study, we have proposed the method combining Euler method and Lyapunov exponent on Poincaré section and evaluated the chaotic state in Izhikevich neuron model. As the result, it has been confirmed that this method can also judge the chaotic state by tuning the initial perturbation against the trajectory.