Local dynamics of a pair of Hutchinson equations with competitive and diffusion coupling

In this paper, we study the dynamics of a system consisting of two coupled Hutchinson equations taking into account the competitive and diffusion coupling between populations. A local asymptotic analysis of the system is performed in the case where the coupling coefficients are small and the parameters of the oscillators are close to the values that provide the Andronov–Hopf bifurcation. We also examine the scenario of phase rearrangements of the system under a change in the diffusion parameter and analyze the dependence of this scenario on the coefficient of competition coupling.