45 citations · 60 across the 4 of their papers we have counts for
5 papers · 1 filter
Dead zones and phase reduction of coupled oscillators
Peter Ashwin, Christian Bick, Camille Poignard
A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in…
State-dependent effective interactions in oscillator networks through coupling functions with dead zones
Peter Ashwin, Christian Bick, Camille Poignard
The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling func…
Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks
Christian Bick, Alexander Lohse
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations s…
Heteroclinic Dynamics of Localized Frequency Synchrony: Heteroclinic Cycles for Small Populations
Christian Bick
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switch…
Asynchronous Networks: Modularization of Dynamics Theorem
Christian Bick, Michael Field
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely…