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Bifurcations in a Leslie-Gower type predator-prey model with a rational non-monotonic functional response

Abstract

A Leslie-Gower type predator-prey model including group defense formation is analyzed. This phenomenon, described by a non-monotonic function originates interesting dynamics; positiveness, boundedness, permanence of solutions, and existence of up to three positive equilibria are established. The solutions are highly sensitive to initial conditions since there exists a separatrix curve dividing their behavior. Two near trajectories can have far omega-limit sets. The weakness of a singularity is established showing two limit cycles can exist. Numerical simulations endorse the analytical outcomes.

Keyword : limit cycles, stability, separatrix, predator-prey model, functional response

How to Cite
González-Olivares, E., Mosquera-Aguilar, A., Tintinago-Ruiz, P. ., & Rojas-Palma, A. (2022). Bifurcations in a Leslie-Gower type predator-prey model with a rational non-monotonic functional response. Mathematical Modelling and Analysis, 27(3), 510–532. https://doi.org/10.3846/mma.2022.15528
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Aug 12, 2022
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