Dynamical behavior of a fractional three-species food chain model

In this paper, a fractional three-species food chain model is considered. The boundedness of the solution of the fractional system has been proven. We analytically determine local and global stability and dynamical behaviors of the equilibria of this system. Further, condition under which a Hopf bifurcation may occur is derived. By using numerical analysis, we figure out that the model may have chaotic dynamics for realistic parameters. Transition to chaotic behavior is established via cycles, period-doubling bifurcation and period-halving bifurcation.