Monotone boundary dynamics generate a unique interior equilibrium and burst in general plant-herbivore models
نویسندگان
چکیده
We investigate two general plant-herbivore models: The 1st model involves a single plant species that has an increasing population dynamics with a decreasing growth function, while the 2nd model has a Holling type III function as its plant’s population dynamics. One key feature of these two models is that the boundary dynamics generate a unique interior equilibrium. The interior equilibrium goes through the Neimak-Sacker bifurcation, which generates limit cycles and periodic orbits. Our study shows that the environmental fluctuations is an important factor to promote the burst population of herbivore for the 1st model. However, the 2nd model does not have such property, instead, it has heteroclinic bifurcation, which is caused by the fact that it has more than 2 boundary equilibria. We also notice that these two models with herbivore attacks plant before or after plant taking up nutrient from soil have similar dynamics. In addition, we compare the dynamics of our models to plant-herbivore models with uni-modal (or multimodal) functions as plant’s dynamics.
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