Numerical analysis of Bazykin–Berezovskaya model

Abstract

In this manuscript, a Bazykin–Berezovskaya model with diffusion by strong Allee effects is studied. Neumann boundary conditions are used to see the positive solution of a diffusion system. Local stability analyses are discussed for all the equilibrium points. The analysis of stability for the proposed scheme is also given. Implicit finite difference schemes like: Euler, Crank–Nicolson (CN) and non-standard finite difference (NSFD) are used to verify the simulation by numerically. A comparison reveals that NSFD method is unconditionally stable for any temporal step-size.

Keywords

• Bazykin–Berezovskaya (BB) model
• backward Euler method
• CN method
• equilibrium points
• NSFD method
• stability analysis