Mathematical Study of Plant-Herbivore-Carnivore System with Holling Type-II Functional Responses

In this paper a systematic study is made, which is aimed at exploring a food chain model related to plants, the herbivore animals and carnivore animals and their impact on the global ecosystem. The study establishes the behavioural dynamics among the three participating species. The proposed model adopts a functional response traceable to Holling type-II for grazing of plants by herbivores and the hunting of the herbivores by the carnivores for their survival. The boundaries of the solution and Hopf bifurcation analysis are discussed at the positive steady state. The persistence (tendency of each specie to resist the invading specie), the global property of dynamic systems is discussed as a part of this study. The statistical randomness of population of each selected specie in the steady state of co-existence due to white noise is also computed. Finally, numerical illustrations are presented to support the results of the study.