Spatiotemporal dynamics and bifurcation analysis on network and non-network environments of a dangerous prey and predator model

Predators in ecological systems frequently confront perilous prey, exposing themselves to the possibility of harm and jeopardizing their own life. Meanwhile, prey endeavour to maximize their reproductive success while minimizing the potential dangers. This work presents a 2D prey–predator model, considering predator interference, the negative impact of fear on prey reproduction, and the consequences of interactions with poisonous prey. The model demonstrates multistability and experiences a range of bifurcations, such as Hopf, transcritical, saddle node, Bogdanov–Takens, cusp, Bautin, and homoclinic bifurcations. The critical parameters might result in the extinction of predators if they suffer excessive losses from interactions with risky prey. It emphasizes the delicate balance that predators must maintain in order to survive. This study explores the expansion of spatial patterns in both network and non-network systems, comparing Turing pattern formation in network models with continuous media and various network topologies. It highlights how Turing patterns are influenced by predator loss, diffusion coefficients, and network topologies. Distinctive patterns, such as spots and stripes, form stably. The simulation shows how different network architectures specifically LA (Lattice), Barabási–Albert (BA), and Watts–Strogatz (WS) networks affect pattern stabilization time and node density distribution. These findings offer vital insights into understanding the complex nature of relationship among prey and predators in ecological systems.