Nonlinear Phenomena in Complex Systems, 2019, Vol.22, No.4, pp.407

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2019, Vol.22, No.4, pp.407 - 412

Infinite Process of Forward and Backward Bifurcations in the Logistic Equation with Two Delays
Ilia Kashchenko and Sergey Kaschenko

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.

Key words: delay differential equation, two delays, small parameter, bifurcations

DOI: https://doi.org/10.33581/1561-4085-2019-22-4-407-412

Full text: Acrobat PDF (2613 KB)