Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect

Abstract

In this paper, a four-species food web model is formulated to investigate the influence of fear effect and nonlinear top predator harvesting on the dynamical behaviors. The global stability of the system at the interior equilibrium is explored by Li–Muldowney geometric approach. By applying the Sotomayor’s theorem, it is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation. The conditions for the occurrence of Hopf bifurcation are established, and the stability of the bifurcating limit cycle is discussed by normal form theory. Finally, the numerical simulations are carried out. It is observed that the system presents chaotic dynamics, periodic window and chaotic attractors. Two distinct routes to chaos are discovered, one is period doubling cascade and the other is the generation and destruction of quasi-periodic states. Moreover, it is found that the fear effect can suppress fluctuations in population density to stabilize the system.