Authors | _ |
---|---|
Journal | Mathematics and computers in simulation |
Page number | 63-76 |
Volume number | 157 |
Paper Type | Full Paper |
Published At | 2019 |
Journal Grade | ISI |
Journal Type | Electronic |
Journal Country | Iran, Islamic Republic Of |
Journal Index | JCR،Scopus |
Abstract
We consider a predator–prey model of Leslie type with ratio-dependent simplified Holling type-IV functional response. The novelty of the model is that the functional response simulates group defense of the prey kind, which in turn, affects permanency of the system and existence of limit cycles. We show that permanency of the system holds automatically for some values of parameters and provides sufficient conditions for global stability of interior equilibrium by constructing a Lyapunov function. We prove that for some values of parameters the system exhibits a Hopf cycle and provides conditions by which the corresponding stable Hopf cycle is the only cycle that model may have. Numerical simulations show that if the conditions are broken, the model may have more than one limit cycle, which is phenomenal among the predator–prey models with one interior equilibrium.
tags: Predator–prey of Leslie type system; Holling type-IV response function; Hopf bifurcation; Permanency