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Recent ecological studies have focused on mathematical modeling, analysis and simulations of thespatial-temporal population distribution of interacting species. In this work, we try to comprehendthe spatiotemporal dynamics that are impacted by the prey-taxis coefficient in an environment wheregeneralist predators induce fear and have carryover effects that trigger both prey and predator populationsto form clusters. By validating the analytical requirements, the suggested model exhibits afinite-time blow-up dependent on initial data. This phenomenon has been numerically confirmed forpredator species. In addition, we expand the spatial model in a discrete environment. Stability analysishas been done for the non-spatial model, the spatial model on networks, and the continuous medium.This study explores the development of spatial patterns in both networked and non-networked environments,specifically comparing the formation of Turing patterns in network framework with thoseobserved in continuous media while considering various network topologies. The combined effects ofthe fear parameter, network structures, and the prey-taxis coefficient are shown to influence Turingpatterns. Different parameter sets cause distinctive patterns, like spots and stripes, to emergegradually. Our simulations demonstrate the effects of various network layouts, namely Lattice (LA),Barabsi-Albert (BA), and Watts-Strogatz (WS) networks, on the node density distribution and thetime needed for patterns to stabilize. We also show how the internal dynamics of networks influencespecies distribution in their environments. These discoveries offer crucial new understandings of theintricate dynamics of prey-predator interactions in ecological networks. |
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