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Bifurcation Chaos"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.1142\/s0218127426500185","type":"journal-article","created":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T10:11:16Z","timestamp":1761905476000},"source":"Crossref","is-referenced-by-count":0,"title":["Re-Examining the Role of the Hill Function in Savanna-Forest Dynamics"],"prefix":"10.1142","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6787-7980","authenticated-orcid":false,"given":"Hao","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. 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