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A General Family of Morphed Nonlinear Phase Oscillators with Arbitrary Limit Cycle Shape

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Noise induced temporal patterns in populations of globally coupled oscillators

Max-Olivier Hongler, Roger Filliger, Philippe Blanchard, Julio Rodriguez

The population dynamics of an assembly of globally coupled homogeneous phase oscillators is studied in presence of non-Gaussian fluctuations. The variance of the underlying stochastic process grows as t + \beta^2 t^2 ( \beta being a constant) and therefore ...

Shaker Verlag2009

Movement Curvature Planning through Force Field Internal Models

Aude Billard, Biljana Petreska von Ritter-Zahony

Human motion studies have focused primarily on modeling straight point-to-point reaching movements. However, many goal-directed reaching movements, such as movements directed towards oneself, are not straight but rather follow highly curved trajectories. T ...

2009

Frequency analysis with coupled nonlinear oscillators

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronizat ...

2008

Spectral coarse graining and synchronization in oscillator networks

Paolo De Los Rios, David Gfeller

Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillat ...

American Physical Society2008

Metastability of fcc-related Si-N phases

The phenomenon of superhardening in TiN/SiNx nanocomposites and the prediction of extreme hardness in bulk gamma-Si3N4 have attracted a large interest to this material system. Attempts to explain the experimental findings by means of first-principles calcu ...

2008

Steady-state Solutions in Mathematical Models of Atrial Cell Electrophysiology and their Stability

Vincent Jacquemet

The steady states of the Fenton–Karma, the Courtemanche and the Nygren cell models were studied by determining the fixed points of the dynamical system describing their cell kinetics. The linear stability of the fixed points was investigated, as well as th ...

2007

Engineering limit cycle systems

Jonas Buchli

In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear ...

EPFL2007

State Space Properties of Transitional Pipe Flow

Tobias Schneider

Transition to turbulence in pipe flow has puzzled scientists since the studies of Hagen, Poiseuille and, most prominently, Osborne Reynolds in the nineteenth century. Much of the difficulty in understanding the transition is connected with the linear stabi ...

2007

Dynamic simulation of regulatory networks using SQUAD

Giovanni De Micheli, Abhishek Garg, Ioannis Xenarios

Background The ambition of most molecular biologists is the understanding of the intricate network of molecular interactions that control biological systems. As scientists uncover the components and the connectivity of these networks, it becomes possible t ...

2007

Dynamic hebbian learning in adaptive frequency oscillators

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for osci ...

2006