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Fast-slow dynamics for intraguild predation models with evolutionary effects. (English) Zbl 1461.34073

A four-dimensional ODE system with one slow and three fast variables is considered. The fast variables describe the dynamics of the prey and two predators, while the slow variable describes the influence of the evolutionary effect. The methods of the geometric theory of singular perturbations are used for a detailed analysis of the behavior of solutions. In particular, the existence of relaxation oscillations has been proved. In conclusion, the problem of the existence of traveling waves is formulated with allowance for diffusion.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C26 Relaxation oscillations for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations

Software:

XPPAUT; GitHub
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Full Text: DOI

References:

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