Impact of Refuge to the Heterogeneous Interaction of Species in Food Chain Model: A Holistic Approach

摘要

This paper deals with the dynamics of a prey dependent three species food chain model involving the Holling type II response function elucidating the impact of refuge constants of prey and predator on the system. We present an exhaustive mathematical explanation of the suggested model to enhance the significance which has originated due to ecological phenomena. Biologically meaningful equilibrium points of the system are endowed along with the behaviors of the system around each equilibrium point. Specifically, boundedness, local and global stability, Hopf bifurcation analysis are performed. Besides, the geometrical significance is provided by all the diagrams supporting the analytical findings. Robustness of the dependence of the system dynamics to each parameter perturbations is presented numerically. Further, the effects of refuge parameters are demonstrated individually as well as simultaneously by two-dimensional and three-dimensional graphs to enhance the impacts more significantly. Moreover, chaotic behavior of the system dynamics is observed for some critical parameter values.