Mathematical analysis of toxin-phytoplankton-fish model with self-diffusion and cross-diffusion

Authors

  • Hamidou Ouedraogo
  • Wendkouni Ouedraogo
  • Boureima Sangare University Nazi BONI

DOI:

https://doi.org/10.11145/j.biomath.2019.11.237

Keywords:

Pattern formation, self-diffusion, cross-diffusion, stability analysis, numerical simulations, toxin-phytoplankton.

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 self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibrium based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation.

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Published

2019-12-16

Issue

Section

Original Articles