Open AccessSpatiotemporal complexity in a predator--prey model with weak Allee effects
Author(s) -
Yongli Cai,
Malay Banerjee,
Yun Kang,
Weiming Wang
Publication year - 2014
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2014.11.1247
Subject(s) - allee effect , constant (computer programming) , hopf bifurcation , instability , functional response , mathematics , statistical physics , predation , predator , bifurcation , physics , nonlinear system , ecology , biology , population , computer science , mechanics , quantum mechanics , demography , sociology , programming language
In this article, we study the rich dynamics of a diffusive predator-prey system with Allee effects in the prey growth. Our model assumes a prey-dependent Holling type-II functional response and a density dependent death rate for predator. We investigate the dissipation and persistence property, the stability of nonnegative and positive constant steady state of the model, as well as the existence of Hopf bifurcation at the positive constant solution. In addition, we provide results on the existence and non-existence of positive non-constant solutions of the model. We also demonstrate the Turing instability under some conditions, and find that our model exhibits a diffusion-controlled formation growth of spots, stripes, and holes pattern replication via numerical simulations. One of the most interesting findings is that Turing instability in the model is induced by the density dependent death rate in predator.