Fast-slow dynamics for intraguild predation models with evolutionary effects
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.
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