Impact of wind in the dynamics of prey–predator interactions

Abstract

The interaction of the predator–prey relationship does not only rely upon the biotic factors, but various abiotic factors can also take an essential role in determining the system dynamics. Wind is an omnipresent component in the biosphere that may crucially alter the predation pattern of any species. In this article, we formulate and analyse a predator–prey model incorporating wind in the predation function. Two types of modified functional responses have been proposed to capture the overall dynamics of the associated system considering the fact that wind may either decrease or increase predation rate of predators. Positivity and boundedness of the solutions of the systems have been shown to confirm the well-posedness of the systems. Equilibrium points and their state of stability have been examined under suitable conditions of parametric restrictions. Wind is shown to change the state of stability of coexistence equilibrium point through Hopf bifurcation in particular cases. On the other hand, strength of wind flow cannot be supposed to be constant throughout a time period. Considering this fact, we further modify the functional responses taken into account periodically varying wind flow and analyse the corresponding systems with the help of computer simulation. Our analysis revealed that the impact of wind on a system dynamics has a strong interrelation with functional response. All the analytical findings have been testified numerically and the article ends with a comprehensive conclusion of our overall study.