Abstract:
One of the most important issues in spatial ecology is to understand how spatial synchrony and dispersalinduced
stability interact. In the existing studies it is shown that dispersion among identical patches results in
spatial synchrony; on the other hand, the combination of spatial heterogeneity and dispersion is necessary for
dispersal-induced stability (or temporal stability). Population synchrony and temporal stability are thus often
thought of as conflicting outcomes of dispersion. In contrast to the general belief, in this present study we
show that mean-field dispersion is conducive to both spatial synchrony and dispersal-induced stability even in
identical patches. This simultaneous occurrence of rather conflicting phenomena is governed by the suppression
of oscillation states, namely amplitude death (AD) and oscillation death (OD). These states emerge through
spatial synchrony of the oscillating patches in the strong-coupling strength. We present an interpretation of the
mean-field diffusive coupling in the context of ecology and identify that, with increasing mean-field density, an
open ecosystem transforms into a closed ecosystem. We report on the occurrence of OD in an ecological model
and explain its significance. Using a detailed bifurcation analysis we show that, depending on the mortality rate
and carrying capacity, the system shows either AD or both AD and OD. We also show that the results remain
qualitatively the same for a network of oscillators. We identify a new transition scenario between the same type
of oscillation suppression states whose geneses differ. In the parameter-mismatched case, we further report on
the direct transition from OD to AD through a transcritical bifurcation. We believe that this study will lead to a
proper interpretation of AD and OD in ecology, which may be important for the conservation and management
of several communities in ecosystems.
