Modeling and analysis of a modified Leslie–Gower type three species food chain model with an impulsive control strategy

• A modified Leslie–Gower type three species food chain impulsive system is studied.
• The dynamical behavior of the system is extensively investigated.
• Sufficient conditions are derived for the global stability and permanence of the system.
• Largest Lyapunov exponent demonstrates the chaotic dynamic behavior of the system.
• Harvesting effort can cause a stable equilibrium to become unstable even a switching of stabilities.

This paper describes a modified Leslie–Gower type three species food chain model with harvesting. We have incorporated impulsive control strategy to the system. Theories of impulsive differential equations, small amplitude perturbation skills and comparison technique are used to study dynamical behavior of the system. Sufficient conditions are derived to ensure global stability of the lowest-level prey and mid-level predator eradication periodic solution. Sufficient conditions are also derived to examine the permanence of the system. Numerical simulations are carried out to verify the analytical results, and the system is analyzed through graphical illustrations. It is observed that the stability of the system exhibits several states, ranging from stable situation to cyclic oscillatory behavior, under different favorable conditions. These results are useful to study the dynamic complexity of ecological systems. The computation of the largest Lyapunov exponent demonstrates the chaotic dynamic nature of the system. The qualitative nature of strange attractor is examined. It is to be noted that the harvesting effort can cause a stable equilibrium to become unstable and even a switching of stabilities.