Instabilities and spatiotemporal patterns behind predator invasions with nonlocal prey competition.
We study the influence of nonlocal intraspecies prey competition on the spatiotemporal patterns arising behind predator invasions in two oscillatory reaction-diffusion integro-differential models. We use three common types of integral kernels as well as develop a caricature system, to describe the influence of the standard deviation and kurtosis of the kernel function on the patterns observed. We find that nonlocal competition can destabilize the spatially homogeneous state behind the invasion and lead to the formation of complex spatiotemporal patterns, including stationary spatially periodic patterns, wave trains and irregular spatiotemporal oscillations. In addition, the caricature system illustrates how large standard deviation and low kurtosis facilitate the formation of these spatiotemporal patterns. This suggests that nonlocal competition may be an important mechanism underlying spatial pattern formation, particularly in systems where the competition between individuals varies over space in a platykurtic manner.
Department of Mathematics, The University of British Columbia, 121–1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2. merchant@math.ubc.ca
Sandra M
SM
Merchant
Wayne
W
Nagata
D000818:Animals; D003163:Competitive Behavior; D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D011235:Predatory Behavior