Chaotic dynamics of a discrete predator–prey system with prey refuge

• Discrete time Prey–predator system with prey refuge is considered here.
• Predator’s attack rate largely varies with the escaping ability of the prey.
• System experiences complex dynamics with varying the strength of prey refuge.
• System experiences Hopf and flip bifurcations.
• The computations of Lyapunov exponent confirms the chaotic dynamics of the system.

Prey–predator system with prey refuge for the case of non-overlapping generations is considered here for our present study. Foraging efficiency of predator largely varies with the escaping ability of the prey from the predator. For this reason system experiences interesting and complex dynamical features with varying the strength of prey refuge, including both population extinction, predator extinction, stable coexistence, multiple invariant closed orbit in different chaotic regions, onset of chaos suddenly and sudden disappearance of the chaotic dynamics. In particular, we observe that when the prey is in stable, oscillatory or even chaotic status, then the predator can tend to extinction. Also, system experiences Hopf-bifurcation and flip bifurcations. Numerical computation is also performed to validate and visualize different theoretical results. The computations of Lyapunov exponent, fractal dimension of the map, recurrence plot and power spectral density confirm the chaotic dynamical behaviors. The analysis and results in this paper are interesting both in mathematics and biology.