In ecological modelling, coupled nonlinear reaction-diffusion systems have been recognized as fundamental tools for generating spatiotemporal patterns. In this study, attention is devoted to a reaction-diffusion system representing interacting species influenced by the Allee effect, incorporating a ratio-dependent functional response and subject to homogeneous Neumann boundary conditions. A thorough investigation is carried out on the asymptotic stability criteria of the corresponding temporal model, with a focus on various bifurcation structures that emerge around the feasible interior equilibrium point. Within the framework of reaction-diffusion modelling, a wide array of complex spatiotemporal patterns-including spot replication, stripes, labyrinthine structures, and others-are explored in the proposed tri-trophic food chain system. A novel spectrum of dynamic behaviour is revealed as a result of the inclusion of the Allee parameter, which gives rise to six distinct pattern transitions, ranging from H π to H 0 . This observation offers a comprehensive progression of spatiotemporal patterns that broadly align with those reported in existing literature. Moreover, the present exploration employs strong and weak Allee effects to comprehend the spatiotemporal pattern structure of reaction-diffusion standpoints and observe that the weak Allee effect discloses more complex dynamic patterns. Extensive numerical simulations are conducted, through which spatiotemporal patterns analogous to those encountered in biological applications are successfully reproduced.
Mandal et al. (Wed,) studied this question.