Destabilization of a seasonal synchronization in a population model with a seasonally varying Allee effect

Climate change causing large seasonal fluctuations is likely to lead to an increase in the average threshold of the Allee effect as well as an increase in its seasonal variability. In this paper, we show that a seasonally synchronized predator-prey system can be strongly destabilized by these changes in the threshold of the Allee effect. The typical result first leads to two-year and multiyear cycles by the principle of period doubling on a folded Möbius strip, up to the emergence of a chaotic and hyper-chaotic attractor living close to the trivial equilibrium corresponding to the extinction of populations. Moreover, this instability of the ecosystem can be hidden for a long time and the transition to its basin of attraction can occur by external perturbation in a random and irreversible manner. We also reveal a double folding of the 1:1 synchronized cycle manifold inside the corresponding Arnold tongue and hysteresis similar to well-known Duffing oscillator.