Hopf bifurcations in a reaction-diffusion population model with delay effect

85Citations
Citations of this article
21Readers
Mendeley users who have this article in their library.

Abstract

A reaction-diffusion population model with a general time-delayed growth rate per capita is considered. The growth rate per capita can be logistic or weak Allee effect type. From a careful analysis of the characteristic equation, the stability of the positive steady state solution and the existence of forward Hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem, where the time delay is used as the bifurcation parameter. The general results are applied to a "food-limited" population model with diffusion and delay effects as well as a weak Allee effect population model. © 2009 Elsevier Inc.

Cite

CITATION STYLE

APA

Su, Y., Wei, J., & Shi, J. (2009). Hopf bifurcations in a reaction-diffusion population model with delay effect. Journal of Differential Equations, 247(4), 1156–1184. https://doi.org/10.1016/j.jde.2009.04.017

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free