Exploring the fixed point theory and numerical modeling of fish harvesting system with Allee effect

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dc.contributor.authorMuhammad Waqas Yasin
dc.contributor.authorMobeen Akhtar
dc.contributor.authorNauman Ahmed
dc.contributor.authorAli Akgül
dc.contributor.authorQasem Al-Mdallal
dc.date.accessioned2025-05-05T12:33:34Z
dc.date.available2025-05-05T12:33:34Z
dc.date.issued2025-04-24
dc.departmentFakülteler, Fen-Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractFish harvesting has a major role in nutritive food that is easily accessible for human nourishment. In this article, a reaction-diffusion fish harvesting model with the Allee effect is analyzed. The study of population models is a need of this hour because by using precautionary measures, mankind can handle the issue of food better. The basic mathematical properties are studied such as equilibrium analysis, stability, and consistency of this model. The Implicit finite difference and backward Euler methods are used for the computational results of the underlying model. The linear analysis of both schemes is derived and schemes are unconditionally stable. By using the Taylor series consistency of both schemes is proved. The positivity of the Implicit finite difference scheme is proved by using the induction technique. A test problem has been used for the numerical results. For the various values of the parameters, the simulations are drawn. The dynamical properties of continuous models, like positivity, are absent from the simulations produced by the backward Euler scheme. Implicit finite difference scheme preserves the dynamical properties of the model such as positivity, consistency, and stability. Simulations of the test problem prove the effectiveness of the Implicit finite difference scheme.
dc.identifier.citationYasin, M. W., Akhtar, M., Ahmed, N., Akgül, A., & Al-Mdallal, Q. (2025). Exploring the fixed point theory and numerical modeling of fish harvesting system with Allee effect. Modeling Earth Systems and Environment, 11(4), 1-18.
dc.identifier.doi10.1007/s40808-025-02398-9
dc.identifier.issn2363-6203
dc.identifier.issn2363-6211
dc.identifier.issue4
dc.identifier.scopus2-s2.0-105003391350
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1007/s40808-025-02398-9
dc.identifier.urihttps://hdl.handle.net/20.500.12604/8647
dc.identifier.volume11
dc.indekslendigikaynakScopus
dc.institutionauthorAkgül, Ali
dc.institutionauthorid0000-0001-9832-1424
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofModeling Earth Systems and Environment
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectAllee effect
dc.subjectAnalysis
dc.subjectBackward Euler scheme
dc.subjectHolling type II
dc.subjectImplicit finite difference scheme
dc.subjectReaction-diffusion model
dc.subjectSimulations
dc.titleExploring the fixed point theory and numerical modeling of fish harvesting system with Allee effect
dc.typejournal-article
oaire.citation.issue4
oaire.citation.volume11

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