Popovych S, Gail A, Schropp J
Mathematical Institute of the University of Cologne, Cologne, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Oct;74(4 Pt 1):041914. doi: 10.1103/PhysRevE.74.041914. Epub 2006 Oct 25.
We study a mathematical model of a single neuron with self-coupling. The model is based on the FitzHugh-Nagumo oscillator and an equation describing synaptic properties of the neuron. The analysis of the model is focused on its dynamics, depending on parameters characterizing synaptic time constants and external signals that affect the neuron. Applying Lyapunov exponents and bifurcation analysis, we point out the occurrence of parameter regions with different behavior such as bursting (chaotic or periodic), spiking, and multistable phenomena. Moreover, we can describe the dynamics of the model using an analytical approximation of the one-dimensional Poincaré map extracted from the numerical simulations.
我们研究了一个具有自耦合的单个神经元的数学模型。该模型基于菲茨休 - 纳古莫振荡器以及一个描述神经元突触特性的方程。对该模型的分析集中在其动力学上，这取决于表征突触时间常数的参数以及影响神经元的外部信号。通过应用李雅普诺夫指数和分岔分析，我们指出了具有不同行为的参数区域的出现，例如爆发（混沌或周期性）、尖峰放电和多稳态现象。此外，我们可以使用从数值模拟中提取的一维庞加莱映射的解析近似来描述该模型的动力学。
