1. Dynamics of a competitive Lotka–Volterra system with three delays
- Author
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Liao, Maoxin, Tang, Xianhua, and Xu, Changjin
- Subjects
- *
BIFURCATION theory , *MANIFOLDS (Mathematics) , *COMPUTER simulation , *EQUILIBRIUM , *MATHEMATICAL formulas , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: In this paper, a competitive Lotka–Volterra system with three delays is investigated. By choosing the sum of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. [Copyright &y& Elsevier]
- Published
- 2011
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