Stochastic prey-predator model with small random immigration

In this paper, we introduce a novel stochastic prey-predator model under random small immigration. Mainly, we prove boundedness for the solution of the model using probabilistic and analytic types of inequalities. Furthermore, possible conditions on the immigration for achieving stochastic square st...

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Main Authors: Alebraheem, Jawdat, Mohammed, Mogtaba, Tayel, Ismail M., Aziz, Muhamad Hifzhudin Noor
Format: Article
Published: AIMS Press 2024
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Online Access:http://eprints.um.edu.my/45836/
https://doi.org/10.3934/math.2024725
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spelling my.um.eprints.458362024-11-13T02:50:20Z http://eprints.um.edu.my/45836/ Stochastic prey-predator model with small random immigration Alebraheem, Jawdat Mohammed, Mogtaba Tayel, Ismail M. Aziz, Muhamad Hifzhudin Noor QA Mathematics In this paper, we introduce a novel stochastic prey-predator model under random small immigration. Mainly, we prove boundedness for the solution of the model using probabilistic and analytic types of inequalities. Furthermore, possible conditions on the immigration for achieving stochastic square stability are obtained. The immigration of both prey and predator is assumed to be either constant and stochastically perturbed or proportional to the population and stochastically perturbed. In all cases, we arrived at the fact that stability can only be achieved if the immigration is small enough. We also show that as random immigration increases, the dynamic becomes destabilized and could lead to chaos. Lastly, we perform a computational analysis in order to verify the obtained theoretical results. AIMS Press 2024 Article PeerReviewed Alebraheem, Jawdat and Mohammed, Mogtaba and Tayel, Ismail M. and Aziz, Muhamad Hifzhudin Noor (2024) Stochastic prey-predator model with small random immigration. AIMS Mathematics, 9 (6). pp. 14982-14996. ISSN 2473-6988, DOI https://doi.org/10.3934/math.2024725 <https://doi.org/10.3934/math.2024725>. https://doi.org/10.3934/math.2024725 10.3934/math.2024725
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Alebraheem, Jawdat
Mohammed, Mogtaba
Tayel, Ismail M.
Aziz, Muhamad Hifzhudin Noor
Stochastic prey-predator model with small random immigration
description In this paper, we introduce a novel stochastic prey-predator model under random small immigration. Mainly, we prove boundedness for the solution of the model using probabilistic and analytic types of inequalities. Furthermore, possible conditions on the immigration for achieving stochastic square stability are obtained. The immigration of both prey and predator is assumed to be either constant and stochastically perturbed or proportional to the population and stochastically perturbed. In all cases, we arrived at the fact that stability can only be achieved if the immigration is small enough. We also show that as random immigration increases, the dynamic becomes destabilized and could lead to chaos. Lastly, we perform a computational analysis in order to verify the obtained theoretical results.
format Article
author Alebraheem, Jawdat
Mohammed, Mogtaba
Tayel, Ismail M.
Aziz, Muhamad Hifzhudin Noor
author_facet Alebraheem, Jawdat
Mohammed, Mogtaba
Tayel, Ismail M.
Aziz, Muhamad Hifzhudin Noor
author_sort Alebraheem, Jawdat
title Stochastic prey-predator model with small random immigration
title_short Stochastic prey-predator model with small random immigration
title_full Stochastic prey-predator model with small random immigration
title_fullStr Stochastic prey-predator model with small random immigration
title_full_unstemmed Stochastic prey-predator model with small random immigration
title_sort stochastic prey-predator model with small random immigration
publisher AIMS Press
publishDate 2024
url http://eprints.um.edu.my/45836/
https://doi.org/10.3934/math.2024725
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score 13.214268