Frontiers in Applied Mathematics and Statistics (Mar 2019)
Chimera States in Ecological Network Under Weighted Mean-Field Dispersal of Species
Abstract
In ecological landscapes, species tend to migrate between nearby patches in search of a better survivability condition. By this dispersal process, they form connectivity between the patches and thereby may develop various correlated or partially correlated population dynamics among species living in the patches. We explore various possible emergent collective population patterns using a simple ecological network model of all-to-all connected patches where we use a particular type of dispersal process that is controlled by a weighted mean-field diffusion to include the failed migration between the interacting patches. We represent the population dynamics of both the predator and prey in each patch by a modified Rosenzweig-MacArthur (mRM) model that incorporates an additional effect of habitat complexity. Our theoretical investigations on the network dynamics, using numerical and to some extent, analytical techniques, show various complex patterns, namely, 2-cluster, 3-cluster and multicluster states, and chimera states, besides synchrony (1-cluster) and homogeneous steady states (HSS) in a migrating metapopulation. An important observation is that addition of habitat complexity in the Rosenzweig-MacArthur (RM) model makes qualitative changes in the collective behaviors. Especially to mention that it shrinks the region of synchrony and broadens the region of HSS, in parameter space and, thereby leads to better survival probabilities and increased population persistence in a natural ecosystem.
Keywords
