Affiliation:
1. Yaroslavl State University
2. National Research Nuclear University MIFI
Abstract
Logistic equation with delay play important role in modelling of various biological processes. In this paper we study the behaviour of solutions of a logistic equation with two delays in a small neighbourhood of equilibrium. The main assumption is that Malthusian coefficient is large, so problem is singular perturbed. To study the local dynamics near points of bifurcation an analogues of normal form was constructed. Its coefficients depends on special bounded discontinues function, which takes all its values infinite number of times when large parameter increases to infinity. It is shown that the system under study has such dynamic effect as infinite process of direct and inverse bifurcations as the small parameter tends to zero.
Publisher
Belarusian State University
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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