Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics
Year: 2019
Author: Wendkouni Ouedraogo, Hamidou Ouedraogo, Wendkouni Ouedraogo, Boureima Sangaré, Boureima Sangaré
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 3 : pp. 207–228
Abstract
In this paper, we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of cross-diffusion on the dynamics of the system. The mathematical study of the model leads us to have an idea on the existence of a solution, the existence of equilibria and the stability of the stationary equilibria. Finally, numerical simulations performed at two-dimensions allowed us to establish the formation of spatial patterns and a threshold of release of the toxin, above which we talk about the phytoplankton blooms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v32.n3.2
Journal of Partial Differential Equations, Vol. 32 (2019), Iss. 3 : pp. 207–228
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Toxin effect
Author Details
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A mathematical analysis of prey-predator population dynamics in the presence of an SIS infectious disease
Savadogo, Assane
Sangaré, Boureima
Ouedraogo, Hamidou
Research in Mathematics, Vol. 9 (2022), Iss. 1
https://doi.org/10.1080/27658449.2021.2020399 [Citations: 5]