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- Title
Rich dynamics in a non-local population model over three patches.
- Authors
Peixuan Weng; Cuntao Xiao; Xingfu Zou
- Abstract
Abstract  We consider a system of nonlinear delay differential equations that describes the growth of the mature population of a species with age-structure living over three patches. We analyze existence of non-negative homogeneous equilibria and their stability and discuss possible Hopf bifurcation from these equilibria. More precisely, by employing both the standard Hopf bifurcation theory and the symmetric bifurcation theory for functional differential equations, we obtain very rich dynamics for the system, including bistable equilibria, transient oscillations, synchronous periodic solutions, phase-locked periodic solutions, mirror-reflecting waves and standing waves.
- Subjects
NONLINEAR differential equations; DELAY differential equations; MATHEMATICAL models of population; HOPF algebras; BIFURCATION theory; TRANSIENTS (Dynamics); PARAMETRONS; STANDING waves; EQUILIBRIUM
- Publication
Nonlinear Dynamics, 2010, Vol 59, Issue 1/2, p161
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-009-9529-5