Nonlinear Dynamics at the Free University Berlin

Summer 2019

Oberseminar Nonlinear Dynamics



Thursday, April 16th Oleh Omel'chenko (Universität Potsdam) Traveling chimera states
We overview recent results about the traveling chimera states observed in a ring of nonlocally coupled phase oscillators with broken reflection symmetry of the coupling kernel. These states manifest themselves as coherence-incoherence patterns moving along the ring. As the coupling asymmetry grows they undergo a sequence of transformations, which can be adequately explained using the continuum limit Ott-Antonsen equation. In the context of this equation the chimera states correspond to its smooth traveling wave solutions. Using the mathematical methods from the PDE and integral equations theory we carry out asymptotic analysis of these traveling waves, describe an algorithm for their numerical continuation and explore the spectrum of the corresponding linearized equation. We show that traveling chimera states can lose their stability via fold and Hopf bifurcations. Some of the Hopf bifurcations turn out to be supercritical resulting in the observation of modulated traveling chimera states.
Tuesday, April 30th Irina Kmit (Humboldt-Universität zu Berlin) Classical bounded and almost periodic solutions to quasilinear first-order hyperbolic systems
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the L2-generalized solutions to the initial-boundary value problems become eventually C2-smooth for any initial L2-data. We investigate small global classical solutions and obtain the existence and uniqueness result under the condition that the evolution family generated by the linearized problem has exponential dichotomy on R. We prove that the dichotomy survives under small perturbations in the leading coefficients of the hyperbolic system. Assuming that the coefficients of the hyperbolic system are almost periodic, we prove that the bounded solution is almost periodic also.
Tuesday, May 28th Sebastian Eydam (WIAS Berlin) Mode-locked solutions and coherence echoes in systems of globally-coupled phase oscillators
In systems of Kuramoto type globally-coupled phase oscillators with equidistant natural frequencies, one can observe an interesting collective phenomenon below the synchronization threshold. The collective behavior is characterized by sharp pulses in the mean-field amplitude and therefore appropriately called mode locked. We discuss the emergence of this particular type of solution as well as the typical bifurcation scenarios that are found along their stability boundaries. In large ensembles, where the natural frequencies follow from a multi-modal distribution, mode-locked solutions are observed and the breakdown of the pulsation due to the broadening of the frequency width is explored. Echo phenomena have a long history and are found in various systems with one of the most prominent examples being the appearance of spin-echoes. We consider an echo-type response phenomenon that occurs after multiple external stimuli in ensembles of phase oscillators below the synchronization threshold. An intuitive explanation of the coherence echo phenomenon in the language of mode locking is given and it is shown that the nonlinear global interaction that supports mode-locked solutions can also enhance the echo response significantly.
Tuesday, June 11th Matthias Wolfrum (WIAS Berlin) Temporal dissipative solitons in systems with time delay
Tuesday, June 25th Stefan Ruschel (TU Berlin) Pulsing dynamics of a laser system with delayed feedback
We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber in the presence of delayed optical self-feedback. We present some recent results regarding the stability and bifurcations of periodic light pulses that are sustained in the external cavity feedback loop, so called external cavity pulse trains.
Friday, July 12th Toshiyuki Ogawa (Meiji University, Tokyo) Drift bifurcation of traveling waves in a reaction-diffusion system with 3 competing species Please note that the seminar takes place at 11:15 a.m. at FU Berlin, Arnimallee 3, room 130, 14195 Berlin.

Time and Place

Talks usually take place on Tuesday at 3:15 p.m. at WIAS Berlin, Mohrenst. 39, Erhard-Schmidt lecture room, 10117 Berlin.

Tea/coffee will be served at 2:45 136.
Guests are always welcome !


switch Last change: Jul. 10, 2019
This page strictly conforms to the HTMLswitch4.01 standard and uses style sheets. Valid HTML 4.01! Valid CSS!