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- Title
Bifurcations and chaotic dynamics in a 4-dimensional competitive LotkaâVolterra system.
- Authors
Ruiping Wang; Dongmei Xiao
- Abstract
Abstract  In this paper, we study the Hopf bifurcation for the four-dimensional competitive LotkaâVolterra system, and give an example which can display chaotic dynamics apparent like Rösslerâs folded band attractor. This demonstrates that Smaleâs conclusions in (J. Math. Biol., 3:5â7, 1976) are true even for the simplest competitive LotkaâVolterra systems when the dimension n is four. We explore the mechanism of occurrence of chaotic behavior for the four-dimensional competitive LotkaâVolterra system. The numerical study indicates that a periodic solution by Hopf bifurcation can undergo successive period-doubling cascades, and a homoclinic orbit can undergo homoclinic bifurcation by Shilânikov theorem.
- Subjects
BIFURCATION theory; CHAOS theory; VOLTERRA equations; H-spaces; NUMERICAL analysis; DIMENSIONAL analysis
- Publication
Nonlinear Dynamics, 2010, Vol 59, Issue 3, p411
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-009-9547-3