Diffusion-driven instability of a predator-prey model with interval biological coefficients

Interval biological coefficients as the imprecise parameters should be considered in biological models since there are various imprecisions in the real world. In this paper, we deal with the pattern dynamics of the predator-prey model with interval biological coefficients and no-flux boundary conditions. We first give the boundedness of the solutions by comparison principle and constructing an invariant rectangle domain with different interval variable values. Then by treating the diffusion coefficient of the predator as the critical parameter, the stable and unstable intervals of the positive equilibrium are discussed. Also, in this manner, the emergence condition of the Turing instability is performed. In the sequel, the amplitude equations around the threshold of the Turing instability are deduced by employing the weakly nonlinear analysis method. In this fashion, the existence and stability of various pattern solutions are classified. Finally, non-symmetrical and symmetrical spatial patterns are displayed with the help of the numerical simulation results in 2D space by choosing different interval biological coefficients.

Automated summary

In this paper, the pattern dynamics of the predator-prey model with interval biological coefficients and no-flux boundary conditions was studied. Boundedness of the solutions was shown by comparison principle and constructing an invariant rectangle domain with different interval variable values. The stable and unstable intervals of the positive equilibrium were discussed by treating the diffusion coefficient of the predator as the critical parameter. Amplitude equations around the threshold of the Turing instability were deduced using weakly nonlinear analysis method to classify the existence and stability of various pattern solutions. Non-symmetrical and symmetrical spatial patterns were displayed in 2D space through numerical simulation results with different interval biological coefficients.