SELF-DIFFUSIVE SPATIOTEMPORAL PATTERNS IN A FOOD CHAIN MODEL THROUGH WEAKLY NONLINEAR ANALYSIS

Shivam (), Teekam Singh, Mukesh Kumar (), Sun-Yuan Hsieh () and Kamred Udham Singh
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Shivam: Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, Uttarakhand 248002, India
Teekam Singh: ��Department of Computer Science and Engineering, Graphic Era (Deemed to be University), 566/6 Bell Road, Clement Town, Dehradun, Uttarakhand 248002, India
Mukesh Kumar: Department of Mathematics, Graphic Era (Deemed to be University), Dehradun, Uttarakhand 248002, India
Sun-Yuan Hsieh: ��Center for Innovative FinTech Business Models, International Center for the Scientific Development of Shrimp Aquaculture, Department of Computer Science and Information Engineering, Institute of Medical Information, Institute of Manufacturing Information and Systems, National Cheng Kung University, Tainan 701, Taiwan
Kamred Udham Singh: �Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan 701, Taiwan¶School of Computing, Graphic Era Hill University, Dehradun, Uttarakhand 248002, India

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-19

Abstract: Density distributions of populations with self-diffusion and interaction in a spatial domain are dynamically visualized with coupled nonlinear reaction–diffusion equations. Incorporating self-diffusion terms creates a more pragmatic modeling paradigm and provides meaningful descriptions of influences on spatiotemporal pattern formation phenomena. This paper examines the effect of self-diffusion in a food chain system with a Holling type-IV functional response and the type of spatial structures forms on a geographical scale due to the random movement of species. We discussed the existence and uniqueness of a positive equilibrium solution and obtained the Turing instability conditions for the self-diffusive food chain model. Moreover, weakly nonlinear analysis close to the Turing bifurcation boundary is used to derive the amplitude equations. The stability of the amplitude equations and sufficient conditions for the emanation of spatiotemporal patterns (such as spots, stripes, and blended patterns) are investigated. The analytical results are verified with numerical simulations. The results are applicable to all environments and can be used to understand the effects of self-diffusion in other food chain models both qualitatively and quantitatively.

Keywords: Food Chain Model; Holling Type IV; Turing Instability; Amplitude Equations; Spatiotemporal Patterns (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500986

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