The Impact of Constant Immigration on a Tri-trophic Food Chain Model
International Journal of Applied and Computational Mathematics
In ecology, simple food chain models are able to produce chaotic dynamics. In the present paper, our aim is to study the impact of constant immigration on a continuous time food chain model that is potentially chaotic. For this, we consider the famous Hastings–Powell model (Ecology 72:896–903, 1991). We observe that immigration has the potential to modify the well-known period-doubling route to chaos by reverse period-halving bifurcation, which may act to prevent the chaotic dynamics. The mathematical features of the Hastings–Powell model with constant immigration are analyzed with the help of stability analysis and bifurcation theory. Extensive numerical simulations are performed to illustrate the dynamics of the system.
Pal, Nikhil; Samanta, Sudip; and Rana, Sourav, "The Impact of Constant Immigration on a Tri-trophic Food Chain Model" (2017). Journal Articles. 2306.