Analytical Investigation of the Chaotic Dynamics of a Two-Dimensional Lotka–Volterra System with a Seasonality Factor

Abstract

The dynamics of the classical biological Lotka–Volterra system with a seasonality factor is investigated analytically. The original model is described by a simple Hamiltonian. To reveal the chaotic behavior in the system, the Hamiltonian is represented by a sum of a Hamiltonian that is independent of time and a number of resonances. The investigation of the interaction of these resonances using Chirikov’s resonance overlap method makes it possible to find an analytical criterion in terms of the critical values of the seasonality amplitudes under which the original system goes to chaos. The results of the study show that in the presence of a periodic perturbation (the seasonality factor in the case under consideration) the system with two dependent variables demonstrates chaotic behavior.