| Abstract: |
| A wide variety of predatory relationships are possible in ecological communities and ecosystems. Intraguild predation, or IGP, represents a combination of predation and competition in which species rely on the same prey resources and benefit from preying on each other. In this talk we shall describe the spatiotemporal dynamics of a three-species reaction-diffusion system, in which the IGP local interaction is of Lotka-Volterra type and the IG-Prey exhibits anti-predator behavior, dispersing along local gradients in predator density.
We first show that the local dynamics support the bistability of the spatially homogeneous coexistence equilibrium with oscillations due to a subcritical Hopf bifurcation.
We demonstrate that the predator avoidance strategy ignites cross-diffusion-driven Turing instability, leading to the emergence of stationary patterns.
Via weakly nonlinear analysis, we derive asymptotic profiles of emergent stationary patterns, revealing that anti-predator behavior can account for the IG-prey and IG-predator segregation patterns observed in the ecology literature. We also prove that the predator avoidance strategy can stabilize coexistence states in IGP communities beyond the conditions imposed by the corresponding spatially homogeneous model.
Finally, we investigate the dynamics near a codimension-two Turing-Hopf point, reproducing the time-oscillatory inhomogeneous structures supported in this regime. |
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