Stability analysis of the coexistence equilibrium of a balanced metapopulation model

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 dispe...

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Bibliographic Details
Published in:Scientific reports 2021-07, Vol.11 (1), p.14084-14084, Article 14084
Main Authors: Rao, Shodhan, Muyinda, Nathan, De Baets, Bernard
Format: Article
Language:English
Subjects:
631/158/1144
631/158/2451
639/705/1041
Coexistence
Differential equations
Dispersal
Equilibrium
Humanities and Social Sciences
Local population
Metapopulations
multidisciplinary
Ordinary differential equations
Science
Science (multidisciplinary)
Stability analysis
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-021-93438-8