Stability of Spiral Chimera States on a Torus

DOI10.1137/17M1141151zbMath1386.37047OpenAlexW2783368931WikidataQ58160559 ScholiaQ58160559MaRDI QIDQ4608080

Edgar Knoblauch, Matthias Wolfrum, O. E. Omel'chenko

Publication date: 15 March 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1141151

zbMATH Keywords

coupled oscillatorsbifurcation analysischimera statescoherence-incoherence patternsOtt-Antonsen equation

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical systems approach to turbulence (76F20) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Dynamical aspects of attractors and their bifurcations (37G35) Ordinary lattice differential equations (34A33) Pattern formations in context of PDEs (35B36)

Related Items (9)

The mathematics behind chimera states ⋮ Chimeras and solitary states in 3D oscillator networks with inertia ⋮ Weak multiplexing in neural networks: Switching between chimera and solitary states ⋮ Nonstationary coherence–incoherence patterns in nonlocally coupled heterogeneous phase oscillators ⋮ The role of timescale separation in oscillatory ensembles with competitive coupling ⋮ Emergence of Stripe-Core Mixed Spiral Chimera on a Spherical Surface of Nonlocally Coupled Oscillators ⋮ Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions ⋮ Mathematical framework for breathing Chimera states ⋮ Spiral wave chimeras induced by heterogeneity in phase lags and time delays

Cites Work

• The dynamics of chimera states in heterogeneous Kuramoto networks
• Symmetry-increasing bifurcation of chaotic attractors
• Singularities and groups in bifurcation theory. Volume II
• Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators
• The chemical basis of morphogenesis
• Chimeras and solitary states in 3D oscillator networks with inertia
• Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators
• Low dimensional behavior of large systems of globally coupled oscillators
• Long time evolution of phase oscillator systems
• Chimeras in Two-Dimensional Domains: Heterogeneity and the Continuum Limit
• CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS

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