- Conference date: 12–14 June 2012
- Location: Kuala Lumpur Convention Centre, Kuala Lumpur, Malaysia
The modelling of prey-predator interactions is of great importance in mathematical ecology, especially when diffusion mechanism and spatial dependence are taken into account. This will lead to reaction-diffusion equations, which the solutions to these equations reveal a broad variety of structures such as instability and pattern formation. In this paper, we wish to study the prey-predator model with two-dimensional diffusion via finite element method. Initially, the algorithm for Galerkin finite element is established and then the finite element discretization is implemented under specified Neumann boundary condition. Simulations are performed to explore the dynamics of two space dimension diffusive prey-predator model. The results of numerical simulations illustrate that the system's behaviour are consistent with the analytically proven theorems. For instance, in the case of equal diffusion constants, the populations of prey and predator has no maximum inside the domain and for 0 < t < T. The maximum is actually dependent on initial conditions. Whilst, in the case predators diffuse faster than preys, we could observe the occurrence of diffusion-driven instability. All these are very interesting to be observed and studied in order to understand the ecological interactions between prey and predator.
- Finite element methods
- Numerical modeling
- Boundary value problems
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