Effectiveness of phase synchronization in chaotic food chain model with refugia and Allee effects during seasonal fluctuations.

Seasonal effects powerfully shape the population dynamics with periodic climate changes because species naturally adjust their dynamics with seasonal variations. In response to these effects, sometimes population dynamics exhibit synchrony or generate chaos. However, synchronized dynamics enhance species' persistence in naturally unstable environments; thus, it is imperative to identify parameters that alter the dynamics of an ecosystem and bring it into synchrony. This study examines how ecological parameters enable species to adapt their dynamics to seasonal changes and achieve phase synchrony within ecosystems. For this, we incorporate seasonal effects as a periodic sinusoidal function into a tri-trophic food chain system where two crucial bio-controlling parameters, Allee and refugia effects, are already present. First, it is shown that the seasonal effects disrupt the limit cycle and bring chaos to the system. Further, we perform rigorous mathematical analysis to perform the dynamical and analytical properties of the nonautonomous version of the system. These properties include sensitive dependence on initial condition (SDIC), sensitivity analysis, bifurcation results, the positivity and boundedness of the solution, permanence, ultimate boundedness, and extinction scenarios of species. The SDIC characterizes the presence of chaotic oscillations in the system. Sensitivity analysis determines the parameters that significantly affect the outcome of numerical simulations. The bifurcation study concerning seasonal parameters shows a higher dependency of species on the frequency of seasonal changes than the severity of the season. The bifurcation study also examines the bio-controlling parameters and reveals various dynamic states within the system, such as fold, transcritical branch points, and Hopf points. Moreover, the mathematical analysis of our seasonally perturbed system reveals the periodic coexistence of all species and a globally attractive solution under certain parametric constraints. Finally, we examine the role of essential parameters that contribute to phase synchrony. For this, we numerically investigate the defining role of the coupling dimension coefficient, bio-controlling parameters, and other parameters associated with seasonality. This study infers that species can tune their dynamics to seasonal effects with low seasonal frequency, whereas the species' tolerance for the severity of seasonal effects is relatively high. The research also sheds light on the correlation between the degree of phase synchrony, prey biomass levels, and the severity of seasonal forcing. This study offers valuable insights into the dynamics of ecosystems affected by seasonal perturbations, with implications for conservation and management strategies.