Complex Dynamics of an Aquatic Tri-Trophic Food Chain System with Holling Type IV Functional Response

Complex dynamics of a modified Hastings-Powell (HP) model (phytoplankton-zooplankton-fish) with Holling type IV functional response are investigated in this article. Boundedness of the system has been established. A detailed study of the boundary equilibrium points and their local stability has been carried out. The condition of uniform persistence of the system has also been derived. Dynamical complexities and subsequent changes in the states of the system have been portrayed using numerical simulation. Modified HP model with Holling type IV functional response gives rise to a similar type of chaotic dynamics (inverted ‘teacup attractor’) as observed in the original HP model with Holling type II functional response. Chaotic or stable dynamics are also numerically verified using Sil’nikov eigenvalue analysis.