A REACTION-ADVECTION-DIFFUSION MODEL IN SPATIAL ECOLOGY: THEORETICAL AND COMPUTATIONAL ANALYSIS

Ishrat  Zahan; Md.  Kamrujjaman; Md. Abdul  Alim

doi:10.53808/KUS.2022.ICSTEM4IR.0131-se

Authors

Ishrat Zahan Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh
Md. Kamrujjaman Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
Md. Abdul Alim Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.53808/KUS.2022.ICSTEM4IR.0131-se

Keywords:

Interaction, resource based advection-diffusion, stability analysis, numerical computations.

Abstract

In a confined heterogeneous habitat with two species interacting for common resources, the research analyzes a reaction-advection-diffusion type dispersal model with homogeneous Neumann boundary conditions for generalized growth functions. Both species follow the same symmetric growths law, but their dispersal strategies and advection rates are different. The following pattern is used to consider the competition strategy: in a bounded heterogeneous habitat, the first population disperses according to its resource functions, whereas the second population disperses according to its carrying capacity. We investigate the model in two scenarios: when carrying capacity and resource functions are non-proportional, competitive exclusion occurs, and one species drives the
other to extinction in the long run for various similar and unequal carrying capacities of competing species. However, coexistence is achievable for different resource distribution consumption if the resource distribution and the carrying capacity phase of the second species are non-constant and similar. A series of numerical computations are used to demonstrate the model’s efficacy in oneand two-dimensional instances, which is particularly significant for environmental consideration.

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