Bifurcation and numerical investigations of diffusive predator-prey model in two space dimension

Abstract

In this article, a two-dimensional reaction-diffusion predator-prey model with ratio-dependent functional response is considered for the numerical study. A time-efficient approximation technique is used to investigate the solution of the underlying system. The proposed approximation technique is developed with the help of nonstandard finite difference rules to solve the predator-prey model under study. The under-discussion numerical approximation method preserves all the solution behavior of the continuous predator-prey system. The numerical stability is also investigated in the model under study and this stability is validated with the graphical solution by using the developed approximation technique. Similarly, bifurcation analysis is discussed numerically. For the comparison of results, two schemes are used namely the forward Euler scheme and the proposed Approximation scheme. The results obtained by the forward Euler scheme are not suitable for the under-consideration model. The results of FE are divergent and negative solutions that are not biologically possible. The results obtained by the proposed Approximation method are consistent, positive, and related to biological phenomena. So, the proposed Approximation scheme has an advantage over the forward Euler scheme, because the proposed method preserves all properties of the continuous model. © 2025 Informa UK Limited, trading as Taylor & Francis Group.