Mean-field dispersion induced spatial synchrony, oscillation and amplitude death, and temporal stability in an ecological model

Background/Question/Methods

One of the most important issues of theoretical as well as applied ecology is how spatial synchrony and dispersal induced stability interact. In the existing studies it is shown that spatial synchrony results in identical patches under dispersion, on the other hand the combination of spatial heterogeneity and dispersion is necessary for dispersal driven stability (or temporal stability). Population synchrony and temporal stability are thus often thought of as conflicting outcomes of dispersion: dispersal can be stabilizing, unless it is synchronizing. In contrast to the general believe in this present study we show that the mean-field dispersion is conducive to both the 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); this states emerge through spatial synchrony of the oscillating patches in the strong coupling strength.

Results/Conclusions

We present an interpretation of 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. For the first time we report the occurrence of OD in theoretical ecology and interpret the significance of the result. Using a detailed dynamical analysis we show that depending upon the mortality rate and carrying capacity the system shows either AD or both AD and OD. We identify a new transition scenario between the same type of oscillation suppression states whose genesis are different. In the parameter mismatched case, we further report 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 is important for the conservation and management of several communities in ecosystems.