Calculating Lyapunov Value for the Logistic Equation with Rapidly Oscillating Delay

Modelirovanie i Analiz Informacionnyh Sistem

N. D. Bykova¹ 

[1] National Research Nuclear University MEPhI;

关键词: averaging;    stability;    nonlinear dynamics;    normal form;   

DOI  :  10.18255/1818-1015-2014-3-121-128

来源: DOAJ

【 摘 要 】

We consider the local dynamic of the logistic equation with rapidly oscillating timeperiodic piecewise constant or piecewise linear coefficient of delay. It was shown that the averaged equation is a logistic equation with two delays in first case and logistic equation with distributed delay in second case. The criterion of equilibrium point stability was obtained in both cases. Dynamical properties of the original equation were considered in the critical case of equilibrium point of averaged equation stability problem. It was shown, that local dynamic in the critical case is defined by Lyapunov value whose sign depends on the parameters of the problem.

【 授权许可】

Unknown