373 citations · 1.6k across the 34 of their papers we have counts for
18 papers · 1 filter
Strong coupling yields abrupt synchronization transitions in coupled oscillators
Jorge L. Ocampo-Espindola, István Z. Kiss, Christian Bick +1
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbat…
Hopf Bifurcations of Twisted States in Phase Oscillators Rings with Nonpairwise Higher-Order Interactions
Christian Bick, Tobias Böhle, Oleh E. Omel'chenko
Synchronization is an essential collective phenomenon in networks of interacting oscillators. Twisted states are rotating wave solutions in ring networks where the oscillator phase…
Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude
Christian Bick, Tobias Böhle, Christian Kuehn
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invari…
Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations
Christian Bick, Tobias Böhle, Christian Kuehn
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave iden…
Network Dynamics with Higher-Order Interactions: Coupled Cell Hypernetworks for Identical Cells and Synchrony
Manuela Aguiar, Christian Bick, Ana Dias
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamic…
Dynamical Systems on Graph Limits and Their Symmetries
Christian Bick, Davide Sclosa
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to…
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…
A General View on Double Limits in Differential Equations
Christian Kuehn, Nils Berglund, Christian Bick +4
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to…
Multi-Population Phase Oscillator Networks with Higher-Order Interactions
Christian Bick, Tobias Böhle, Christian Kuehn
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe rea…
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…
Functional Asynchronous Networks: Factorization of Dynamics and Function
Christian Bick, Michael Field
In this note we describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional a…
Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling
Peter Ashwin, Christian Bick, Oleksandr Burylko
For a system of coupled identical phase oscillators with full permutation symmetry, any broken symmetries in dynamical behaviour must come from spontaneous symmetry breaking, i.e.…
Isotropy of Angular Frequencies and Weak Chimeras With Broken Symmetry
Christian Bick
The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition of a weak chimera…
Chaotic Weak Chimeras and their Persistence in Coupled Populations of Phase Oscillators
Christian Bick, Peter Ashwin
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoheren…
Asynchronous Networks and Event Driven Dynamics
Christian Bick, Michael Field
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a…