Colloquium Talk - Dr. Xiaoying Wang

Title: Complex patterns in a resource-consumer model with short reproduction season

Speaker: Dr. Xiaoying Wang
              Department of Mathematics and Statistics
              University of Ottawa

Abstract: Spatial heterogeneous distribution of organisms is commonly seen in nature. The reasons underlying such heterogeneity motivate extensive studies. In this paper, we propose an impulsive reaction-diffusion equation model for a resource-consumer system to study pattern formation in a homogeneous landscape. We consider that the reproduction and dispersal of the consumer happen at distinct stages, and the reproduction season is short whereas the dispersal stage is long. Analytical results and numerical simulations show that pattern formation is possible for the system if ratio-dependent functional response is chosen. More importantly, pattern formation may occur if the consumer and the resource diffuse at a comparable scale, which is different from the continuous time analogy. Furthermore, numerical simulations show that low over-winter survival rate of the resource promotes the occurrence of pattern formation. This suggests that spatial patterns may emerge more easily due to the discontinuity in population densities.