Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains

Feltrin, Guglielmo; Zanolin, Fabio

doi:10.1007/s11784-022-00984-3

Cited by 1 publication

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“…To apply the Brouwer fixed-point theorem [57][58][59] we need the set [ min k j 2N , max k j ] N to be compact and convex, which is obviously true, and the mapping Π t : […”

Section: Existence and Uniqueness Steady-state Pointsmentioning

confidence: 99%

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Korotkov,

Petrovskii

2023

Mathematics

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Major threats to biodiversity are climate change, habitat fragmentation (in particular, habitat loss), pollution, invasive species, over-exploitation, and epidemics. Over the last decades habitat fragmentation has been given special attention. Many factors are causing biological systems to extinct; therefore, many issues remain poorly understood. In particular, we would like to know more about the effect of the strength of inter-site coupling (e.g., it can represent the speed with which species migrate) on species extinction or persistence in a fragmented habitat consisting of sites with randomly varying properties. To address this problem we use theoretical methods from mathematical analysis, functional analysis, and numerical methods to study a conceptual single-species spatially-discrete system. We state some simple necessary conditions for persistence, prove that this dynamical system is monotone and we prove convergence to a steady-state. For a multi-patch system, we show that the increase of inter-site coupling leads to the formation of clusters—groups of populations whose sizes tend to align as coupling increases. We also introduce a simple one-parameter sufficient condition for a metapopulation to persist.

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“…To apply the Brouwer fixed-point theorem [57][58][59] we need the set [ min k j 2N , max k j ] N to be compact and convex, which is obviously true, and the mapping Π t : […”

Section: Existence and Uniqueness Steady-state Pointsmentioning

confidence: 99%

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Korotkov,

Petrovskii

2023

Mathematics

View full text Add to dashboard Cite

show abstract

Equilibrium points, periodic solutions and the Brouwer fixed point theorem for convex and non-convex domains

Cited by 1 publication

References 44 publications

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

Extinctions in a Metapopulation with Nonlinear Dispersal Coupling

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