Positive solutions and pattern formation in a diffusive tritrophic system with Crowley–Martin functional response

In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin functional response under mixed boundary conditions. Using degree theory and fixed point index-based methods, we have proved the existenc...

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Bibliographic Details
Published inNonlinear dynamics Vol. 100; no. 1; pp. 763 - 784
Main Authors Kumari, Nitu, Mohan, Nishith
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2020
Springer Nature B.V
Subjects
Automotive Engineering
Boundary conditions
Classical Mechanics
Control
Dynamical Systems
Engineering
Fixed points (mathematics)
Food chains
Mechanical Engineering
Original Paper
Pattern analysis
Stability analysis
Vibration
Pattern formation
Reaction diffusion system
Degree theory
Global attractor
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Summary:In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin functional response under mixed boundary conditions. Using degree theory and fixed point index-based methods, we have proved the existence of the positive solutions of the proposed system. We have proved the permanence of the positive solutions and existence of global attractor. The conditions for diffusion-driven instability have been obtained analytically. Moreover, the pattern formation due to diffusion-driven instability has been investigated numerically. We have shown the existence of the positive solutions both analytically and numerically.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05534-5