Department: Department of Mathematics            PI's Name: Jia-Yuan Dai

Journal: Mathematische Annalen, 391, 6373–6399; https://link.springer.com/article/10.1007/s00208-024-03081-7

Title: Hybrid bifurcations: periodicity from eliminating a line of equilibria

Abstract: Jia-Yuan Dai, in collaboration with Alejandro López Nieto, Phillipo Lappicy, Nicola Vassena, and Hannes Stuke, has successfully established a theoretical framework for hybrid bifurcations and revealed a novel mechanism for the emergence of periodic orbits in smooth dynamical systems.

Hybrid bifurcations arise from the combination of a bifurcation without parameters and a classical parameter-dependent bifurcation. The main contribution of this paper is a complete classification of the hybrid bifurcations that occur when a line of equilibria with an exchange point of normal stability disappears. Considering a predator-prey system with Holling’s type II functional response as a concrete example, we have proved the existence and stability of new coexisting periodic orbits, thereby demonstrating the effectiveness and considerable potential of hybrid bifurcation theory in applications.