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Summer 2023
Oberseminar Nonlinear Dynamics
Organizers
Program
Appointments only by arrangement.
| Tuesday, June 27th |
Jia-Yuan Dai (National Chung Hsing University, Taiwan) |
Exploring a new mechanism of periodic orbits: Dynamics of two predators competing for a prey
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| We prove the existence of stable periodic orbits of an ODE system that describes the dynamics of two predators competing for the same prey. The prey population grows logistically in the
absence of predation and the predators feed on the prey with Holling 's type-II nonlinearity. We explain how stable periodic orbits, located far away from the boundary planes, are triggered by
perturbing an elliptic Hopf bifurcation point without parameters. To this end, we prove that the ODE system admits an elliptic Hopf bifurcation and the existence and stability of periodic orbits are ensured
by the averaging method. This is a joint work with A. López Nieto, P. Lappicy, H. Stuke, and N. Vassena.
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Phillipo Lappicy (Universidad Complutense de Madrid, Spain) |
On the exceptional Bianchi models
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| Most (if not all) rigorous results regarding spatially homogeneous and anisotropic cosmological singularities are based on the Bianchi types VIII and IX models, which constitute four-dimensional
dynamical systems. However, there is one exceptional model which has the same dimensionality, but with almost no rigorous results: the Bianchi type VI_{-1/9} models. These exceptional
models should play a distinguished role in the generic asymptotic dynamics towards cosmological singularities, especially when small spatial inhomogeneities are considered. We will discuss
some early explorations/findings which are based on joint work with C. Uggla.
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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: Jun. 21, 2023
