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A prey‐predator model with diffusion and a supplementary resource for the prey in a two‐patch environment

    J. Dhar Affiliation

Abstract


In this paper, a prey‐predator dynamics, where the predator species partially depends upon the prey species, in a two patch habitat with diffusion and there is a non‐diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both the species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases.


Plėšrūno-aukos modelis su difuzija ir papildomu resursu aukai dviejų sričių areale


Santrauka



Šiame straipsnyje modeliuojama ir analizuojama plešrūnu ir auku dinamika, laikant, kad plešrūnų populiacija dalinai priklauso nuo aukų skačiaus. Arealą sudaro dvi sritys, kuriose vyksta populiacijų individų difuzija, be to, aukoms yra išskirtas nedifunduojantis resursas.


Įrodyta, kad egzistuoja teigiamas, monotoniškas, tolydus stacionarusis sprendinys, tenkinantis tolydumo sąlyga abiems populiacijoms atskirai. Gautos asimptotinio stabilumo sąlygos tiesiniu ir netiesiniu atvejais.


First Published Online: 14 Oct 2010

Keyword : Population diffusion, patchiness, supplementary resource, steady state solution, stability

How to Cite
Dhar, J. (2004). A prey‐predator model with diffusion and a supplementary resource for the prey in a two‐patch environment. Mathematical Modelling and Analysis, 9(1), 9-24. https://doi.org/10.3846/13926292.2004.9637238
Published in Issue
Mar 31, 2004
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