Nonlinear Dynamics at the Free University Berlin

Summer 2023

Oberseminar Nonlinear Dynamics



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
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.
Phillipo Lappicy (Universidad Complutense de Madrid, Spain) On the exceptional Bianchi models
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.

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.

Guests are always welcome !


switch Last change: Jun. 21, 2023
This page strictly conforms to the XHTMLswitch1.0 standard and uses style sheets. Valid XHTML 1.0! Valid CSS!