Isolating patterns in a reaction-diffusion system with Smith population growth

The present article concerns itself with the theoretical investigation on an interacting species model system with special emphasis on the species growth followed by Smith and a constant proportion of prey refuge. The prime objective of the study is to provide an adequate mathematical framework in order to carry out a comprehensive analytical investigation of the dynamical complexity between predator and prey species. The proposed model system is not only explored in the perception of diverse local bifurcations in a two-dimensional plane but also of the global bifurcations about coexistence equilibria under specific parametric conditions. For the purpose of validation of all the analytical outcomes together with the applicability of the model concerned, a quantitative sensitivity analysis based on numerical simulation is performed. The evolution of diffusion-driven pattern formation in two-dimensional plane in terms of spot, stripe, labyrinthine, stripe-hole mixture and hole replication as well is patently exhibited. These patterns are all influenced by both the Smith growth principle and prey refuge of the diffusive system. Finally, the influence of model parameters of significance on the dynamics of the proposed model system is, however, not ruled out to depict graphically from the present study.