Stability of amplitude chimeras in oscillator networks

Abstract

We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size $N=12$ exhibiting amplitude chimeras

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Cited by in corpus (6)

• Distinct collective states due to the trade-off between attractive and repulsive couplings
• Control of amplitude chimeras by time delay in dynamical networks
• Networks of coupled oscillators: from phase to amplitude chimeras
• Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators
• Amplitude chimera and chimera death induced by external dynamical agents
• Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings