Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 70, Issue 2, Pages 658-670Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2008.01.002
Keywords
Hopf bifurcation; Stability; Competition system; Delay
Categories
Funding
- National Science Foundation of China [60771026]
- Science Foundations of Shanxi Province [2007011019]
- Special Scientific Research Foundation [20060110005]
- Program for New Century Excellent Talents in University [NCET050271]
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In this paper, Hopf bifurcation for two-species Lotka-Volterra competition systems with delay dependence is investigated. By choosing the delay as a bifurcation parameter, we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form, i.e., there are periodic solutions bifurcating out from the positive equilibrium. Our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter. Further, an explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds, and numerical simulations supporting the theoretical analysis are also given. (C) 2008 Elsevier Ltd. All rights reserved.
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