Chaotic Dynamics of a Forest Growth Model With Variable Mortality Rate

ABSTRACT In this paper, we study the dynamics of a degenerate reaction‐diffusion system modeling the evolution in time and space of a forest ecosystem. This forest model admits a mortality rate that is variable in space, to better take into account the heterogeneity of the environment, and presents an original chaotic dynamic. We establish a novel result of the existence of heterogeneous stationary solutions and prove that they exhibit chaotic behavior in space. This spatial chaos is numerically simulated and interpreted with an ecological approach, in regard to observed heterogeneous patterns in forest ecosystems. We analyze the stability of the extinction equilibrium and establish sufficient conditions to guarantee the persistence of the forest ecosystem. We also prove a comparison principle that clarifies the effect of an increase in tree mortality on the behavior of the solutions. Finally, we experiment with the convergence of the solutions towards heterogeneous and chaotic patterns.