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Research Article Open access CC BY 4.0

Competitive Reaction-diffusion Systems: Travelling Waves and Numerical Solutions

Md. Kamrujjaman, Asif Ahmed, Shohel Ahmed

Advances in Research · pp. 1–12 · Published 20 Aug 2019

10.9734/air/2019/v19i630140

Abstract

In this paper, we consider a competitive reaction-diffusion model to describe the existence of travelling wave solutions of two competing species. Moreover, the non-linear system is also studied by introducing different competitive-cooperative coefficients; constant and spatially distributed which leads to the persistence and extinction of organisms in a heterogeneous environment of population biology. If the diffusion coefficients and other parameters are positive constant, it is seen that one species is in extinction by the other and coexistence is also possible under certain conditions on carrying capacity. The results are numerically investigated by using the Finite difference method (FDM).

Nonlinear PDEs travelling wave solutions reaction-diffusion Crank-Nicolson scheme.

References (14)

  1. 1 Numerical Analysis
  2. 2 Shock Waves and Reaction—Diffusion Equations [DOI]
  3. 3 Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems [DOI]
  4. 4 Nonlinear Parabolic and Elliptic Equations [DOI]
  5. 5 Front Propagation in Heterogeneous Media [DOI]
  6. 6 An Application of the Generalized Morse Index to Travelling Wave Solutions of a Competitive Reaction-Diffusion Model.
  7. 7 Traveling wavefronts in diffusive and cooperative Lotka–Volterra system with delays [DOI]
  8. 8 Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering [DOI]
  9. 9 Travelling waves in a model of species migration [DOI]
  10. 10 On a competitive system with ideal free dispersal [DOI]
  11. 11 Dynamics of a diffusive competition model in spatially heterogeneous environment [DOI]
  12. 12 A mathematical analysis on public goods games in the continuous space [DOI]
  13. 13 Weak Competition and Ideally Distributed Populations in a Cooperative Diffusive Model with Crowding Effects [DOI]
  14. 14 Exactly Solvable Models of Biological Invasion [DOI]

Cited by 3

Interplay of harvesting and the growth rate for spatially diversified populations and the testing of a decoupled scheme.

Md Mashih Ibn Yasin Adan, Md. Kamrujjaman, M. Molla · Mathematical biosciences and engineering : MBE · 2023

The role of harvesting and growth rate for spatially heterogeneous populations

Md. Mashih Ibn Yasin Adan, Md. Kamrujjaman, M. Molla · arXiv.org · 2022

Lyapunov Stability Analysis of a Competition Model with Crowding Eects

Md. Kamrujjaman∗a, Kamrun Nahar Keya, M. Islam · GANIT Journal of Bangladesh Mathematical Society · 2021

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