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Dynamical behaviors in the FitzHugh–Nagumo system with a memory trace

物理 摄动(天文学) 振幅 振荡(细胞信号) 量子电动力学 数学分析 数学 量子力学 遗传学 生物
作者
Yuan Gao,Jun Liu,Shuijing Wang,Shaopeng Yang,Guangrui Wang,Hongmei Zhang
出处
期刊:International Journal of Modern Physics B [World Scientific]
卷期号:35 (25)
标识
DOI:10.1142/s0217979221502593
摘要

In this paper, the dynamical behaviors of the FitzHugh–Nagumo (FHN) system with a memory trace, which has time-fractional derivatives, are investigated. For the case of a classical order, the constant input current can change the stability of the equilibrium point in a single FHN unit, and the equilibrium is unstable in a certain range of the current. A decrease of the order of the time-fractional derivative may lead to a linear reduction of the range and the appearance of a solution of mixed-mode oscillations, which consist of subthreshold small-amplitude oscillation and suprathreshold large-amplitude oscillation. In the parameter space of the input current and the fractional order, the region of existing the mixed-mode oscillation is linearly widened when the fractional order moves toward its small value. If a suprathreshold perturbation is periodically applied, there exist some obvious bands, on which the excited period is locked to the perturbation period according to some rational ratios. As a result, the bands can be narrowed by decreasing the value of fractional order and their location has a slight drift toward the small value of the perturbation period. In addition, the properties of solitary traveling waves and wave train solutions are also studied in the one-dimensional space. It is illustrated that the traveling pulse is wider for a smaller value of fractional order, and its velocity is larger. Further, some relations of wave trains have a great change when the value of the fractional order is changed.
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