神经元模型的复杂动力学:分岔与编码

COMPLEX DYNAMICS OF THE NEURONAL MODEL:BIFURCATION AND ENCODING

研究了改进的Morris-Lecar(ML)神经元模型的放电节律模式和模式转化的峰峰间期(interspike intervals,ISIs)分岔结构,通过调节模型中的两个重要参数μ和Vk,发现对于固定的μ,改变Vk,神经元呈现出从倍周期级联分岔到加周期分岔的复杂结构,放电模式从静息态转化为周期、混沌簇放电状态;若选取此分岔过程中的某一Vk值,对μ进行调节,呈现出的ISIs分岔结构在很大程度上取决于单个神经元的放电节律模式,且单个神经元处于混沌簇放电时,μ带来的分岔动力学行为较丰富.由于神经元能够通过动作电位对信息进行编码,所以我们推测,研究神经元的放电节律模式和动作电位的ISIs分岔结构能为理解神经信息编码机制提供线索.

Firing rhythm patterns and the interspike intervals （ISis） bifurcation structures of the action potential in the modified Morris - Lecar （ML） neuronal model are investigated. By modulating two important control parameters μ and Vk, we find that for some fixed μ, varying Vk, the neuron exhibits a cascade of period doubling bifurcation and period -adding bifurcation leading the system from the silent regime to a periodic and chaotic state dominated by bursting events; While,if we take some peculiar values of Vk based on the former bifurcation diagram, modulating/x can lead to a variety of bifurcation structures which have something to do with the single neuron＇ s firing patterns, moreover, chaotic bursting brings us much richer bifurcation dynamics than periodic bursting. We know that neurons can encode information by use of action potentials, based on this, we infer that study of firing rhythm patterns and ISis structures can be a clue to understand the mechanism of the neuronal encoding.