Slow-fast analysis of a modified Leslie-Gower model with Holling type I functional response

In this paper, we consider a modified Leslie-type prey-generalist predator system with piecewise-smooth Holling type I functional response. Considering the reproduction rate of the prey population higher than that of the predator, the model becomes a slow-fast system that mathematically leads to a singular perturbation problem. To analyse the stability of the boundary equilibrium on the switching boundary, we use a generalized Jacobian that enables us to investigate how the eigenvalues jump at the boundary point. We investigate the slow-fast system by employing geometric singular perturbation theory and blow-up technique that reveal a wide range of interesting complicated dynamical phenomena. We have studied existence of saddle-node bifurcation, Bogdanov-Takens bifurcation, bistability, singular Hopf bifurcation, canard orbits, multiple relaxation oscillations, saddle-node bifurcation of limit cycle and boundary equilibrium bifurcations. Numerical simulations are carried out to substantiate the analytical results.

Automated summary

This paper investigates a modified Leslie-type prey-generalist predator system with piecewise-smooth Holling type I functional response. By employing geometric singular perturbation theory and blow-up technique, a wide range of interesting and complicated dynamical phenomena are revealed. Numerical simulations are performed to validate the analytical results.