Re-Examining the Role of the Hill Function in Savanna-Forest Dynamics

In this paper, we investigate the dynamics of an ODE model to re-examine the role of Hill function in the transition dynamics of grassland and forest ecosystems by using a hierarchical parametric analysis method. We present a comprehensive analysis of the model’s global dynamics, including the number and stability of equilibria, the absence of limit cycles, and the presence of saddle-node bifurcations. In particular, we analyze codimension-2 and -3 cusp bifurcations and highlight the significance of bistable regions in savanna models, which enhance the robustness of these biological systems. Furthermore, we introduce a new measure of parameter resilience of the savanna-forest system to describe its own transition of bistable region and robustness. Finally, we explore the effect of seasonality on the savanna system, revealing that it can exhibit a single equilibrium or more complex scenarios with two or three coexisting equilibria. Our findings may provide valuable insights into the coexistence of savanna and forest ecosystems.