论文标题
二维离散神经元模型的拓扑数分析
Topological-numerical analysis of a two-dimensional discrete neuron model
论文作者
论文摘要
我们对Chialvo于1995年引入的神经元的二维模型进行了计算机辅助分析（混乱，孤子和分形5，461-479）。我们将方法应用于Arai等人介绍的基于设定的拓扑方法对全球动力学进行严格分析。 2009年（Siam J. Appl。Dyn。Syst。8，757-789），然后改进和扩展。此外，我们引入了一种新算法，以分析链条复发集中的返回时间。基于此分析，以及有关链条复发集大小的信息，我们开发了一种新方法，允许人们确定可能出现混乱动力学的参数子集。这种方法可以应用于各种动态系统，我们讨论了其一些实际方面。本文中描述的数据和软件可在http://www.pawelpilarczyk.com/neuron/上获得。
We conduct computer-assisted analysis of the two-dimensional model of a neuron introduced by Chialvo in 1995 (Chaos, Solitons & Fractals 5, 461-479). We apply the method for rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 (SIAM J. Appl. Dyn. Syst. 8, 757-789) and improved and expanded afterwards. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects. The data and the software described in the paper are available at http://www.pawelpilarczyk.com/neuron/.
