Special Session 5: New trends in pattern formations and dynamics for dissipative systems and related topics
Hybrid bifurcations: Periodicity from Eliminating a Line of Equilibria
Jia-Yuan Dai
National Tsing Hua University Taiwan
Co-Author(s): Alejandro L\`{o}pez-Nieto, Phillipo Lappicy, Nicola Vassena, Hannes Stuke, Jia-Yuan Dai
Abstract:
We describe a new mechanism that triggers periodic orbits in smooth dynamical systems. To this end, we introduce the concept of hybrid bifurcations, which consists of a bifurcation without parameters and a classical bifurcation. Our main result classifies the hybrid bifurcation when a line of equilibria with an exchange point of normal stability vanishes. We showcase the efficacy of our approach by proving stable periodic coexistent solutions in an ecosystem of two competing predators with Holling`s type II functional response.