2020/04/25 by Kaijen Cheng, Cheng, Kaijen, Hongming You +3
Biochemistry, Genetics and Molecular Biology · Environmental Science · Medicine · #Animal Ecology and Behavior Studies #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2004.12237
openalex publication_date 2020/04/25 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28
In this work, we revisit the classical Holling type II three species food chain model with a different viewpoint. Two critical parameters λ1 and λ2 dependent on other six parameters are defined. We show that local stabilities and existence of all equilibria can be reformulated by λ1 and λ2, and the complete classifications of parameters and its corresponding dynamics are given. Three global extinction results are showed by comparison principle analytically. Moreover, some interesting numerical simulations, including the chaotic phenomena, and the bi-stability phenomena, including equilibrium-cycle bi-stability and cycle-cycle bi-stability, are presented numerically. Finally, a brief discussion and biological implications are given.