7 papers
Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations
Sindre W. Haugland, Katharina Krischer
Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We…
The changing notion of chimera states, a critical review
Sindre W. Haugland
Chimera states, states of coexistence of synchronous and asynchronous motion, have been a subject of extensive research since they were first given a name in 2004. Increased intere…
Between Synchrony and Turbulence: Intricate Hierarchies of Coexistence Patterns
Sindre W. Haugland, Anton Tosolini, Katharina Krischer
Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexis…
2-Cluster Fixed-Point Analysis of Mean-Coupled Stuart-Landau Oscillators in the Center Manifold
Felix P. Kemeth, Bernold Fiedler, Sindre W. Haugland +1
We reduce the dynamics of an ensemble of mean-coupled Stuart-Landau oscillators close to the synchronized solution. In particular, we map the system onto the center manifold of the…
Global heteroclinic rebel dynamics among large 2-clusters in permutation equivariant systems
Bernold Fiedler, Sindre W. Haugland, Felix P. Kemeth +1
We explore equivariant dynamics under the symmetric group of all permutations of elements. Specifically we study one-parameter vector fields, up to cubic order, which com…
Cluster singularity: the unfolding of clustering behavior in globally coupled Stuart-Landau oscillators
Felix P. Kemeth, Sindre W. Haugland, Katharina Krischer
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembl…