Bifurcations and Pattern Formation in a Predator–Prey Model

• DOI: 10.1142/s0218127418501407
• Publication Date: 2018-10-25T01:56:02Z
• Authors: Yongli Cai; Zhanji Gui; Xuebing Zhang; Hongbo Shi; Weiming Wang
• Keywords: Transcritical bifurcation; Pitchfork bifurcation; Bogdanov–Takens bifurcation; Homoclinic bifurcation; Center manifold

In this paper, we investigate the spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating prey refuge subject to Neumann boundary conditions. We mainly consider Hopf bifurcation and steady-state which bifurcate from constant positive model. case bifurcation, by center manifold theory normal form method, establish direction stability bifurcating periodic solutions; in local global theories, prove existence find that there are two typical bifurcations, Turing Turing–Hopf bifurcation. Via numerical simulations, exhibits not only stationary pattern induced diffusion is dependent on space independent time, but also temporal time space, both space. These results may enrich formation