16 research outputs found
Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling
We study a system of four identical globally coupled phase oscillators with
biharmonic coupling function. Its dimension and the type of coupling make it
the minimal system of Kuramoto-type (both in the sense of the phase space's
dimension and the number of harmonics) that supports chaotic dynamics. However,
to the best of our knowledge, there is still no numerical evidence for the
existence of chaos in this system. The dynamics of such systems is tightly
connected with the action of the symmetry group on its phase space. The
presence of symmetries might lead to an emergence of chaos due to scenarios
involving specific heteroclinic cycles. We suggest an approach for searching
such heteroclinic cycles and showcase first examples of chaos in this system
found by using this approach.Comment: 18 pages, 8 figure
Synchronization in oscillatory networks
The formation of collective behavior in large ensembles or networks of coupled oscillatory elements is one of the oldest and most fundamental aspects of dynamical systems theory. Potential and present applications span a vast spectrum of fields ranging from physics, chemistry, geoscience, through life- and neurosciences to engineering, the economic and the social sciences. This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or the heart muscle - to name but a few. This book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models
Sequential activity and multistability in an ensemble of coupled Van der Pol oscillators
In this paper collective dynamics of an ensemble of inhibitory coupled Van der Pol oscillators are studied. It was found that a stable heteroclinic contour and a stable heteroclinic channel between saddle cycles exist. These heteroclinic structures are responsible for the sequential activity of different oscillations. The corresponding bifurcations leading to the appearance of heteroclinic trajectories are analyzed