Nonlinear Dynamics at the Free University Berlin

Winter 2020/2021

Oberseminar Nonlinear Dynamics



Tuesday, November 17th, 15:15 Prof. Dr. Angela Stevens (Universität Münster) Mathematical modeling of regeneration phenomena in biology
Some organisms can regenerate from nearly any kind of severe injury. Regeneration does not function this way in humans. Understanding the underlying mechanisms in model organisms like flatworms is therefore of strong interest. In our mathematical model differences between bulk and tissue surface dynamics play an important role and will be discussed in detail. Joint work with Arnd Scheel.
Tuesday, November 24th Dr. Giulia Ruzzene (Universitat Pompeu Fabra, Barcelona and IFISC, Palma de Mallorca) Control of chimera states in multilayer networks
Chimera states are one of the most intriguing and studied types of partial synchronization. In small systems, which are the most relevant for experimental situations, chimera states present various instabilities. Therefore, it is natural to investigate methods to control them. We propose a control mechanism based on the idea of a pacemaker oscillator, which allows to control the position of a chimera state within a network and to prevent its collapse to the fully synchronous state. We show how this mechanism developed for ring networks of phase oscillators can be applied to multilayer networks with more complex node dynamics, such as FitzHugh-Nagumo oscillator. In particular, we show that it allows to remotely control a chimera state in one layer via a pacemaker in the other layer.
Tuesday, December 1st Dr. Felix Kemeth (Johns Hopkins University) 2-Cluster Fixed-Point Analysis of Mean-Coupled Stuart-Landau Oscillators in the Center Manifold
Clustering in phase oscillator systems with long-range interactions has been subject to theoretical investigations for many years. By mapping the dynamics of mean-coupled Stuart-Landau oscillators onto the center manifold of the Benjamin-Feir instability, we aim to add to the theoretical understanding of clustering in systems beyond phase oscillator ensembles. In particular, we discuss the formation of 2-cluster states in this lower dimensional manifold and outline the resulting implications for the dynamics of the coupled oscillator ensemble. Joint work with Bernold Fiedler, Katharina Krischer and Sindre Haugland.
Tuesday, December 8th Elisenda Feliu (University of Copenhagen) Understanding of bistability and Hopf bifurcations in biochemical reaction networks
In the context of (bio)chemical reaction networks, the dynamics of the concentrations of the chemical species over time are often modelled by a system of parameter-dependent ordinary differential equations, which are typically polynomial or described by rational functions. The polynomial structure of the system allows the use of techniques from algebra to study properties of the system around steady states, for arbitrary parameter values. In this talk I will present the formalism of the theory of reaction networks, and how applied algebra plays a role in the study of three main questions: determination of bistability, determination of Hopf bifurcations, and parameter regions for multistationarity. I will present new results tackling these questions by using a ubiquitous and challenging network from cell signaling (the dual futile cycle) as a case example. For this network, which is relatively small, several basic questions, such as the existence of oscillations, the parameter region of multistationarity, and whether multistationarity implies bistability, remain unresolved. The results I will present arise from different joint works involving Conradi, Kaihnsa, Mincheva, Sadeghimanesh, Torres, Yürük, Wiuf and de Wolff.
Tuesday, January 12th Serhiy Yanchuk (Technical University Berlin) Delay systems and machine learning applications
A single dynamical system with time-delayed feedback (DDE) can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups. The first setup is the reservoir computing where the DDE plays the role of a high-dimensional reservoir that performs specific computational tasks. We discuss which dynamical properties of such a reservoir are important. These properties include the conditional Lyapunov exponents and the eigenvalue spectrum of the linearized DDE. The second setup is the Deep Neural Network, which can be emulated with a DDE. We present a method for folding a deep neural network of arbitrary size into a single neuron with multiple time-delayed feedback loops. This single-neuron deep neural network consists of only a single nonlinearity and appropriately adjusted modulations of the feedback signals. The connection weights are determined via a modified back-propagation algorithm that we have developed for such networks.
Tuesday, January 19th Dr. Michal Hadrava (Institute of Computer Science of the Czech Academy of Sciences, Prague) A Dynamical Systems Approach to Spectral Music: Modeling the Role of Roughness and Inharmonicity in Perception of Musical Tension
Tension-resolution patterns seem to play a dominant role in shaping our emotional experience of music. Whereas in traditional Western music, these patterns are mainly expressed through harmony and melody, many contemporary musical compositions (e.g. so-called "spectral music") employ sound materials lacking any perceivable pitch structure, rendering these two compositional devices useless. Motivated by recent advances in music-theoretical and neuroscientific research into the related phenomenon of dissonance, we propose a neurodynamical model of musical tension based on a spectral representation of sound and hence applicable to any kind of sound material, pitched or non-pitched.

Time and Place

Because of the current Corona virus situation, the events take place online.

Guests are always welcome !


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