Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections

This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological view point, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.