Premium
Turing instability and Hopf bifurcation in a diffusive Leslie–Gower predator–prey model
Author(s) -
Peng Yahong,
Liu Yangyang
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3853
Subject(s) - mathematics , hopf bifurcation , ode , pitchfork bifurcation , instability , bifurcation , stability (learning theory) , mathematical analysis , saddle node bifurcation , nonlinear system , physics , mechanics , quantum mechanics , machine learning , computer science
In this paper, a reaction‐diffusion predator–prey system that incorporates the Holling‐type II and a modified Leslie‐Gower functional responses is considered. For ODE, the local stability of the positive equilibrium is investigated and the specific conditions are obtained. For partial differential equation, we consider the dissipation and persistence of solutions, the Turing instability of the equilibrium solutions, and the Hopf bifurcation. By calculating the normal form, we derive the formulae, which can determine the direction and the stability of Hopf bifurcation according to the original parameters of the system. We also use some numerical simulations to illustrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.