Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh-Rose neuron model

• Published in: Chinese physics B Vol. 23; no. 3; pp. 179 - 185
• Main Author: 贾冰
• Format: Journal Article
• Language: English
• Published: 01.03.2014
• Subjects: Bifurcations; Chaos theory; Computer simulation; Firing; Mathematical models; Neurons; Pacemakers; Two dimensional; 参数空间; 实验鉴定; 时间序列分析方法; 梳形; 模型模拟; 混沌区域; 神经元模型; 钙离子浓度
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/23/3/030505

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.