Nonlinear Dynamics at the Free University Berlin

Winter 2013/14

Oberseminar Nonlinear Dynamics



Oct 22, 2013 Oleksandr Burylko
(National Academy of Sciences Kyiv, Ukraine)
Analysis of bifurcations and the study of competition in phase oscillator networks with positive and negative coupling
A globally coupled phase oscillators of Kuramoto type with positive (conformist) and negative (contrarian) couplings are considered in (Hong & Strogatz (HS), 2011). Here we generalize the HS system to include a phase shift at the interaction function. The system is analyzed by using bifurcation theory as well as a detailed study of geometry of the invariant manifolds. Results include a rich repertoire of dynamical regimes (multistability, complex heteroclinic cycles, chaos, etc). Some of these interesting regimes are not possible in HS system.
Oct 28, 2013
Alexander Skubachevskii
(Peoples' Friendship University of Russia, Russia)
The Vlasov–Poisson equations in infinite cylinder and controlled plasma
We consider the first mixed problem for the Vlasov-Poisson equations in infinite cylinder, describing evolution of densities for ions and electrons in rarefied plasma with external magnetic field. We construct in explicate form a stationary solution with densities of charged particles in interior cylinder. In a neighborhood of stationary solution it is proved existence and uniqueness of classical solution with supports of densities of charged particles locating at some positive distance from cylindrical boundary. This work was supported by the RFBR (grant No. 12-01-00524).

Talk will take place at 3:15 p.m. at the Free University Berlin, Room 140, Arnimallee 7 (rear building), 14195 Berlin.
Oct 28, 2013
Dmitrii Turaev
(Imperial College London, UK)
Arnold diffusion in the a priori chaotic case
Let a real-analytic Hamiltonian system have a normally-hyperbolic cylinder such that the Poincare map on the cylinder has a twist property. Let the stable and unstable manifolds of the cylinder intersect transversely. The homoclinic channel is a small neighbourhood of the union of the cylinder and the homoclinic. We show that generically (in the real-analytic category) in the channel there always exist orbits which deviate from the initial condition unboundedly.

Talk will take place at 4:45 p.m. at the Free University Berlin, Room 140, Arnimallee 7 (rear building), 14195 Berlin.
Oct 29, 2013 SFB 647 und Workshop am WIAS
Nov 5, 2013 DFG Research Center MATHEON - Center Days
Nov 12, 2013 CANCELLED
Nov 19, 2013 Antonio Politi
(University of Aberdeen, UK)
Coarsening processes in Discrete Nonlinear Schroedinger-type models
The Discrete Nonlinear Schroedinger equation (DNLSE) is a paradigmatic model used to describe both Bose-Einstein condensates and propagation in waveguides. The DNLSE behaviour is discussed from the point of view of statistical mechanics, with a particular emphasis given to the convergence to the equilibrium state in the regime of the so-called negative (absolute) temperatures. The observed coarsening is studied with the help of simplified models of exclusion-process type.
Nov 26, 2013 SFB 647
Dec 3, 2013 CANCELLED
Dec 10, 2013 CANCELLED
Dec 17, 2013
3:15 p.m.
Atsushi Mochizuki
(RIKEN Advanced Science Institute, Japan)
Rate sensitivity of biochemical reaction systems: A function-free approach
Dec 17, 2013
4:45 p.m.
Jan Sieber
(University of Exeter, UK)
Periodic orbits in equations with state-dependent delay
Jan 7, 2014 SFB 647
Jan 14, 2014 CANCELLED
Jan 21, 2014 Josef Ladenbauer
(Technical University Berlin)
Modeling populations of adaptive neurons: spike train properties and network dynamics
Many types of neurons exhibit spike rate adaptation, a gradual decrease in spiking activity following a sudden increase in stimulus intensity. This phenomenon is typically produced by slowly deactivating transmembrane potassium currents, which effectively inhibit neuronal responses and can be controlled by neuromodulators. In this talk I will present recent theoretical work on (networks of) model neurons, showing (i) how these adaptation currents change the relationship between fluctuating synaptic input, spike rate output and the spike train statistics of single neurons and (ii) how they contribute to spike synchronization as well as spike rate oscillations in recurrent networks of excitatory and inhibitory neurons.
Jan 28, 2014 Philipp Hövel
(Technical University Berlin)
Dynamics of two neural oscillators in the presence of heterogeneous coupling delays
Investigations of nonlinear dynamics in coupled systems have seen a huge increase in interest during the last years. The size of considered systems ranges from a few coupled elements to complex networks, and collective dynamics may arise in various patterns, of which in-phase (or zero-lag) synchronization is just the most prominent one. The signal transmission between coupled elements is often not instantaneous. Thus, non-zero transmission times have to be taken into account as crucial quantities that influence the dynamics of network nodes to a large extent.

In this presentation, I will discuss synchronization effects in the presence of delayed coupling for two excitable neural systems. In particular, I will investigate the effects of heterogeneous delays in the coupling [1]. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. I will present an analysis of this behavior based on the interplay of the different time delays. The numerical results are supported by analytical findings. In addition, I elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.

[1] A. Panchuk, D. P. Rosin, P. Hövel, and E. Schöll: Synchronization of coupled neural oscillators with heterogeneous delays Int. J. Bif. Chaos 23, 1330039 (2013).
Feb 4, 2014 SFB 647
Feb 11, 2014 Irina Kmit
(Humboldt University Berlin)
Hopf bifurcation for one-dimensional hyperbolic PDEs

Time and Place

Talks usually take place on Tuesday at 3:15 p.m.
at the Weierstraß Institute
Ehrhard-Schmid-Hörsaal, Mohrenstr. 39, 10117 Berlin.

Tea and coffee will be served at 2:45 p.m. on the ground floor.
Guests are always welcome !


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