1. Stability analysis of the coexistence equilibrium of a balanced metapopulation model
- Author
-
Nathan Muyinda, Bernard De Baets, and Shodhan Rao
- Subjects
0106 biological sciences ,Lyapunov function ,DYNAMICS ,PROMOTES ,Science ,GAME ,Metapopulation ,010603 evolutionary biology ,01 natural sciences ,Stability (probability) ,Article ,03 medical and health sciences ,symbols.namesake ,DISPERSAL ,Stability theory ,COMPETITIVE NETWORK ,Statistical physics ,SCISSORS ,030304 developmental biology ,Mathematics ,Ecological modelling ,Equilibrium point ,0303 health sciences ,Multidisciplinary ,COMPLEX ,CONSEQUENCES ,Invariance principle ,Ode ,INTRANSITIVITY ,Applied mathematics ,Mathematics and Statistics ,Ordinary differential equation ,symbols ,PAPER ,Medicine ,Theoretical ecology - Abstract
We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.
- Published
- 2021