Metapopulation dynamics with detrimental impact of the resources on the consumers
摘要
We consider a coupled Rosenzweig-MacArthur model that incorporates the negative impact of resources on consumers. This negative effect of resources has been empirically examined within various ecological systems and has also been referred to as unidirectional mutualisms. We show that the employed model exhibits both symmetry preserving, and symmetry breaking oscillatory states. We also exhibit the extreme multistable nature of the dynamical states, which includes regions of birhythmicity and rhythmogenesis in suitable parameter ranges. Further, we illustrate the emergence of distinct inhomogeneous and homogeneous stable steady states as a function of the mean-field dispersal rate. The observed states serve as alternative states for the population abundance thereby promoting the persistence of the metacommunity. The dynamical transitions between these states are mediated by distinct bifurcation scenarios. We also examine the impact of the carrying capacity of the habitats and the mortality rate of the consumer on the observed dynamical states, in addition to the impact of the positive and negative efficiency rate of the resources on the consumers of the metapopulation. We derive the analytical stability condition for the transcritical and saddle-node bifurcation curves by performing a linear stability analysis of the homogeneous steady states.