Dynamical behavior of fractional-order Hastings–Powell food chain model and its discretization

• New discretization method for the fractional-order Hastings–Powell food chain model.
• Existence and uniqueness of solutions of the proposed system are discussed.
• Local stability of the fractional and discretized systems is investigated.
• Maximal Lyapunov exponents are calculated for the fractional and discretized systems.
• Conditions of Hopf bifurcation are obtained for the discretized fractional system.

In this work, the dynamical behavior of fractional-order Hastings–Powell food chain model is investigated and a new discretization method of the fractional-order system is introduced. A sufficient condition for existence and uniqueness of the solution of the proposed system is obtained. Local stability of the equilibrium points of the fractional-order system is studied. Furthermore, the necessary and sufficient conditions of stability of the discretized system are also studied. It is shown that the system’s fractional parameter has effect on the stability of the discretized system which shows rich variety of dynamical behaviors such as Hopf bifurcation, an attractor crisis and chaotic attractors. Numerical simulations show the tea-cup chaotic attractor of the fractional-order system and the richer dynamical behavior of the corresponding discretized system.