Dynamics of Leslie–Gower type generalist predator in a tri-trophic food web system

• Leslie–Gower type generalist predator in tri-trophic food web system.
• Existence of Andronov-Hopf bifurcation in planes.
• Existence of “Snail-shell” chaotic attractor.
• Existence of very high Lyapunov exponents values.

In this paper, the dynamics of a tri-trophic food web system consists of Leslie–Gower type generalist predator has been explored. The system is bounded under certain conditions. The Hopf-bifurcation has been established in the phase planes. The bifurcation diagrams exhibit coexistence of all three species in the form of periodic/chaotic solutions. The “snail-shell” chaotic attractor has very high Lyapunov exponents. The coexistence in the form of stable equilibrium is also possible for lower values of parameters. The two-parameter bifurcation diagrams are drawn for critical parameters.