Chaos in the three-species Sokol-Howell food chain system with fear

In this paper, the influence of predation fear on the dynamics of the three species food chain system is formulated mathematically and investigated. It is assumed that the food is transferred from the lower level to the upper level according to the Sokol-Howell type of functional response due to the anti-predator property of each prey in the system. The boundedness and persistence conditions are established for the proposed food chain system. The local and global stability analysis is investigated. The occurrence conditions of local bifurcation including the Hopf bifurcation near the equilibrium points are obtained. In the end, numerical simulation is performed to validate the theoretical results and present the dynamical behavior of the system. Different mathematical tools such as strange attractor, bifurcation diagram, and Lyapunov exponents are used to detect chaos in the proposed system. It is observed that the model is capable of exhibiting complex dynamics including chaos. It is also pointed out that a suitable predation fear can control the chaotic dynamics and make the system stable.