Destabilization of a population model due to a seasonally varying Allee effect impacting seasonal synchronization

Extreme weather conditions due to climate change lead to seasonal variations in species’ life cycles. It can impact the distribution and abundance of populations by influencing their habitats and food sources, leading to changes in the timing of biological processes like reproduction and migration. It can impact the ecosystem by altering species interactions between prey and predator. Populations in these habitats typically coordinate their behaviors in accordance with the shifting seasons. Ecological synchrony’s durability with increasing temperatures and climate change impacts is a crucial topic. In this talk, I will present a predator-prey interaction model that includes a seasonally changing Allee effect to investigate the impact of seasonality. The typical result first includes the presence of two-year and multiyear cycles through a period-doubling cascade on a folded M¨obius strip. This process persists until a chaotic and hyper-chaotic attractor emerges close to the trivial equilibrium, causing population extinction. Demonstrating changes in the Allee effect threshold will reveal significant destabilization of the seasonally synchronized predator-prey system. Additionally, dynamical investigations have shown hysteresis similar to the well-known Duffing oscillator and a twofold folding of the 1:1 synchronized cycle manifold within the related Arnold tongue. In the second half, the interactive model will be extended to include a metapopulation structure with populations distributed across two patches and connected through cross-coupling, often called cross-predation. Cross-coupling refers to the alternative for predators in each specific patch. Finally, the impact of coupling on multiyear cycles and chaotic attractors will be studied to ascertain if the coupling mechanism can prevent population extinction.