Influence of Allee Effect on Extreme Events in Coupled Three Species Systems

Abstract

We consider the dynamics of two coupled three-species population patches, incorporating the Allee Effect, focussing on the onset of extreme events in the coupled system. First we show that the interplay between coupling and the Allee effect may change the nature of the dynamics, with regular periodic dynamics becoming chaotic in a range of Allee parameters and coupling strengths. Further, the growth in the vegetation population displays an explosive blow-up beyond a critical value of coupling strength and Allee parameter. Most interestingly, we observe that beyond a threshold of coupling strength and Allee parameter, the population densities of all three species exhibit non-zero probability of yielding extreme events. The emergence of extreme events in the predator populations in the patches is the most prevalent, and the probability of obtaining large deviations in the predator populations is not affected significantly by either the coupling strength or the Allee effect. In the absence of the Allee effect the prey population in the coupled system exhibits no extreme events for low coupling strengths, but yields a sharp increase in extreme events after a critical strength of coupling. The vegetation population in the patches display a small finite probability of extreme events for strong enough coupling, only in the presence of Allee effect. Lastly we consider the influence of additive noise on the continued prevalence of extreme events. Very significantly, we find that noise suppresses the unbounded vegetation growth that was induced by a combination of Allee effect and coupling. Further, we demonstrate that noise mitigates extreme events in all three populations, and beyond a noise level we do not observe any extreme events in the system at all. This finding has important bearing on the potential observability of extreme events in natural and laboratory systems.