Threshold dynamics of the plant-herbivore interaction with Allee effect

Abstract

Different species, like plants and herbivores, that are occupying similar ecosystems and living among each other interact regularly. In this interaction, understanding the conditions in which coexistence equilibrium occurs answers a key question in Ecology. In the interaction between plants and herbivores, plants serve as food for herbivores on the food chain. Then the livelihood of herbivores highly depend on the availability of food, in this case the availability of plants. With this motivation, we reformulated a mathematical model which assumes that the death rate of herbivore population is dependent on plant density. Moreover, the abundance of the plant density alone does not guarantee the non-extinction of the herbivore population as they are assumed to reproduce sexually. Therefore, we also included the concept of Allee effect for the herbivore population in the model. Using the mathematical theory of dynamical systems, threshold conditions and trapping region are obtained to ensure coexistence of the population. Moreover, it has been shown that the dynamics of the population is sensitive to the feeding rate of herbivore