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The authors investigate emergent spatial patterns in an augmented predator-prey system with external food by analyzing a reaction-diffusion model incorporating Holling type II predation and intraspecific predator competition. Through analytical Hopf and Turing bifurcation calculations, they prove that predator self-limitation prevents unbounded population growth, driving a transition from spatially uniform limit cycles to stationary Turing patches as prey mobility and competition increase. At the codimension-2 Turing-Hopf crossover point, the interaction of oscillatory and spatial instabilities produces dynamically pulsing spatiotemporal patterns, demonstrating that predator self-competition is the decisive control parameter for spatial community organization.
Intraspecific predator competition serves as the master switch for emergent spatial structure in resource-augmented ecosystems, dictating clean phase transitions between synchronized field oscillations, static high-density patches, and dynamic breathing waves.
Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.