A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment

Amartya Das and G.P. Samanta

Physica A: Statistical Mechanics and its Applications, 2020, vol. 538, issue C

Abstract: Refuge for prey and additional food for predator together with environmental fluctuation is a very interesting topic for dynamical system. In this work we have studied a prey–predator model in presence of some additional food to predators and incorporating refuge for prey which protects certain amount of prey. In this model prey grows logistically in absence of predator. Functional response of predator towards additional food and prey is derived considering mutual interference among the individuals of the predator. We have introduced Gaussian white noise to model the influence of environmental fluctuations on the growth rate of prey and the death rate of predator. We have shown, how Gaussian white noise plays an important role for extinction and persistence of the system. Some important properties such as positivity, boundedness, uniform continuity etc. of the solution are proved. In extinction scenario we have found that extinction of prey population propel predator population to extinct. It is considered that prey refuge depends on biomass of prey and predator population both. In numerical simulation we have justified how this consideration is more actual to the reality. Also it is shown the importance of additional food to predator as prey may not be available (prey may get refuge) for predation.

Keywords: Additional food; Prey refuge; Itô formula; Global solution; Persistence; Extinction (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119316188

DOI: 10.1016/j.physa.2019.122844

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