Impact of seasonal variability of sea waves on the dynamics of a predator-prey system

In this work, a predator-prey model has been proposed to study the impact of sea wave on the system dynamics. Since the predation success of predator species is inextricably related with the amount of sea wave, so a predation efficiency function of wave flow has been introduced in the model system. The well-posedness of the proposed system has been established by proving the positivity, boundedness, and persistence properties. All the equilibrium points have been found along with their parametric conditions of existence. The local stability analysis of all the equilibrium points and global stability analysis of the interior equilibrium point have been studied. Both the analysis of trans-critical bifurcation and Hopf-bifurcation have been performed in a systematic way. It can be seen from the model analysis that the stability of the system dynamics is greatly influenced by both the wave and conversion rate parameters. Additionally, the wave parameter has an immense impact on the population densities of both species. Furthermore, a non-autonomous version of the suggested model system has been created by using the wave flow parameter as a time-dependent periodicity function to take into account the seasonality phenomenon. It has been discovered that the seasonally-forced system exhibits a wide spectrum of dynamical scenarios including bursting phenomenon in the system dynamics. All of the analytical results have been supported suitably by extensive numerical simulations.