Seasonal wind-induced dynamics in a tri-trophic food chain: exploring bifurcation

Abstract

This study examines the dynamics of a tri-trophic food chain, specifically examining the effect of fluctuating wind conditions on middle and top predators’ success in predation. Wind flows impact predator success, increasing intra-specific competition within predator groups. Additionally, wind intensity is modeled as a time-dependent parameter, reflecting that it varies over time. We established well-posedness, which includes positivity, boundedness, dissipativity, and uniform persistence. After that, we determined the equilibria and demonstrated their local and global stability. Hopf bifurcation of the system was established and analyzed through analytical methods. Numerical simulations of our system demonstrate how variations in wind flow intensity and intra-specific competition drive the model to undergo Hopf bifurcation. We observed that the model experienced two Hopf bifurcations concerning this wind speed parameter. Moreover, we demonstrate that wind intensity directly affects middle and top predator populations and their ability to survive. Additionally, our numerical simulations revealed that the seasonality parameter introduces periodic solutions at the stable modes of the model system. In contrast, it generates complex dynamics at the unstable modes, with varying wind levels and increased seasonal wind strength acting as potential factors influencing the extinction or survival of both predator species.