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Winter 2024/2025
Oberseminar Nonlinear Dynamics
Organizers
Program
Appointments only by arrangement.
| Tuesday, January 14th |
Jia-Yuan Dai (National Tsing Hua University) |
Hybrid bifurcations: Periodicity from eliminating a line of equilibria
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| 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. This is a joint work with Alejandro López Nieto, Phillipo Lappicy, Nicola Vassena, and Hannes Stuke.
Reference:
A. López Nieto, P. Lappicy, N. Vassena, H. Stuke, and J.-Y. Dai. Hybrid Bifurcations: Periodicity from Eliminating a Line of Equilibria. https://arxiv.org/pdf/2310.19604
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Nicola Vassena (Universität Leipzig) |
Takens-Bogdanov points and Global Hopf bifurcation in reaction networks
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| TIn this talk, I will explore two distinct yet complementary approaches for identifying periodic solutions in ODE systems arising from reaction networks. The first method focuses on locating an equilibrium where the Jacobian has an algebraically double eigenvalue zero (a Takens-Bogdanov point). The second method examines changes in stability at an equilibrium with an invertible Jacobian, leading to global Hopf bifurcation. I will discuss how -- perhaps not so surprisingly?- the sufficient conditions for these two bifurcations overlap
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Time and Place
Talks usually take place on Tuesday at 3:15 p.m.
at the Free University Berlin
Arnimallee 7 (rear building), room 140.
WIAS, Mohrenstr. 39, Erhard-Schmidt lecture room, 10117 Berlin.
The event is also accessible via Zoom.
Guests are always welcome !
Archive
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Last change: Jan. 9, 2025
