Savanna Dynamics with Grazing, Browsing, and Migration Effects

This article explores the dynamics of savanna ecosystems with grazing,\nbrowsing, and migration effects. Covering over one-eighth of the Earth's land\narea and supporting about one-fifth of the global population, the savanna is an\necological system whose importance has only recently garnered significant\nattention from biologists. The interactions between organisms in this ecosystem\nare highly complex, and fundamental mathematical issues remain unresolved. We\nrigorously analyze traveling waves in savanna systems and focus on whether\ntrees, grass, grazers, and browsers coexist. We demonstrate the existence of\nvarious traveling waves, including waves transitioning from extinction to\nco-existence and waves from a grass-vegetation state (where only grass and\ngrazers exist) to co-existence. Due to the biodiversity of species in grassland\necosystems, it is not appropriate to consider overly simplified models of\ncompetition between grasses and trees. From both a biological and mathematical\nperspective, factors such as animal grazing, browsing, and migration (which\nfacilitates seed dispersal) play a crucial role in promoting ecological\nstability and coexistence. Additionally, we estimate the nonzero minimum value\nof the total plant biomass within the savanna dynamic system to better\nunderstand the persistence and stability of sustainable development within the\necosystem.\n