Abstract
A discrete metapopulation model with temporal dependent migration is proposed in order to study the stability of synchronized dynamics. During each time step, we assume that there are two processes involved in the population dynamics: local patch dynamics and migration process between the patches that compose the metapopulation. We obtain an analytical criterion that depends on the local patch dynamics (Lyapunov number) and on the whole migration process. The stability of synchronized dynamics depends on how individuals disperse among the patches.
Highlights
The forms of dispersion in a metapopulation system can induce the whole system to multiple behaviors [1, 3, 4, 7, 13]
An interesting behavior related to the dispersal process is the synchronized dynamics where the populations in all patches evolve with the same density [11]
In this paper we develop a model of a network of equal patches linked by temporal dependent migration
Summary
The forms of dispersion in a metapopulation system (populations of single-species that live in fragments called patches) can induce the whole system to multiple behaviors [1, 3, 4, 7, 13]. A well-documented example is the Canadian lynxes that presents synchronized dynamics in its densities fluctuations due to weather conditions [2, 11]. Another example is the vole populations in Norway that synchronize due to dispersal processes and birds predation [8]. In [4] was obtained an analytical result for the stability of synchronized trajectories by considering a model with an arbitrary number of patches linked by dispersal. An analytical result examining a special case of density-dependent dispersal was obtained in [13], concluding that this mechanism reduces the stability regions of the synchronous dynamics.
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