Local-nonlocal interaction and spatial-temporal patterns in single species population over a patchy environment. (English) Zbl 0859.34056
A system of functional differential equations is proposed to describe the dynamics of a single-species population distributed over a patchy environment. Of major concern is the impact of the interaction between local aggregation and global delayed competition on the dynamics and the spatial-temporal patterns of the considered system. It is shown that the spatially heterogeneous steady state solutions can bifurcate from a spatially homogeneous steady state solution if the dispersion rate is large. Moreover, Hopf bifurcation of periodic solutions including phase-locked oscillations and synchronous oscillations can occur when the time delay in the global intraspecies competition reaches a critical value. Examples are provided to exhibit the complexity of the dynamics and the co-existence of phase-locked oscillations and heterogeneous steady state solutions.
Reviewer: M.Lizana (Merida)
MSC:
34K13 | Periodic solutions to functional-differential equations |
34K18 | Bifurcation theory of functional-differential equations |
34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
34C23 | Bifurcation theory for ordinary differential equations |