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Volume 32, Issue 3
Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics

Hamidou Ouedraogo, Wendkouni Ouedraogo & Boureima Sangaré

DOI: 10.4208/jpde.v32.n3.2

J. Part. Diff. Eq., 32 (2019), pp. 207-228.

Published online: 2019-10

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  • 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.

  • Keywords

Toxin effect populations dynamics predator-prey model reaction-diffusion system bifurcation pattern formation.

  • AMS Subject Headings

65P30, 68Q85, 68U20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ameldo16@yahoo.fr (Hamidou Ouedraogo)

wendkounio@yahoo.fr (Wendkouni Ouedraogo)

mazou1979@yahoo.fr (Boureima Sangaré)

  • BibTex
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  • TXT
@Article{JPDE-32-207, author = {Ouedraogo , HamidouOuedraogo , Wendkouni and Sangaré , Boureima}, title = {Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {3}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n3.2}, url = {http://global-sci.org/intro/article_detail/jpde/13340.html} }
TY - JOUR T1 - Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics AU - Ouedraogo , Hamidou AU - Ouedraogo , Wendkouni AU - Sangaré , Boureima JO - Journal of Partial Differential Equations VL - 3 SP - 207 EP - 228 PY - 2019 DA - 2019/10 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n3.2 UR - https://global-sci.org/intro/article_detail/jpde/13340.html KW - Toxin effect KW - populations dynamics KW - predator-prey model KW - reaction-diffusion system KW - bifurcation KW - pattern formation. AB -

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.

Hamidou Ouedraogo , Wendkouni Ouedraogo & Boureima Sangaré . (2019). Bifurcation and Stability Analysis in Complex Cross-Diffusion Mathematical Model of Phytoplankton-Fish Dynamics. Journal of Partial Differential Equations. 32 (3). 207-228. doi:10.4208/jpde.v32.n3.2
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