Chimera states induced by spatially modulated delayed feedback

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 6, 2010, Pages

  Omel'Chenko, Oleh E ^a,b,c   Maistrenko, Yuri L ^c   Tass, Peter A ^b,d,e  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

^c INSTITUTE OF MATHEMATICS   (Ukraine)

^d UNIVERSITY OF COLOGNE   (Germany)

^e Brain Imaging Center West   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

A-STABILITY; COHERENT STATE; DELAYED FEEDBACK; INCOHERENT STATE; NUMERICAL APPROACHES; SELF-CONSISTENCY; SPATIOTEMPORAL PATTERNS;

NUMERICAL ANALYSIS;

EID: 78651381800     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.066201     Document Type: Article

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58. Solving the discretized spectral problem, we obtain in this case the pseudocontinuous spectrum which is separated from the imaginary axis and lies completely in the LHP. However, we presume that for larger delays the behavior of the spectrum may be different. In particular, the pseudocontinuous spectrum may cross the imaginary axis, resulting in a Turing-like bifurcation scenario for chimera states. We plan to address this issue in a future study.
59. We recall that in our settings the chimera state is described as a standing-wave solution to system; therefore, we use here the term "torus bifurcation" to distinguish this bifurcation of a periodic orbit from the classical Hopf bifurcation of a fixed point. The latter also appears in our analysis, but for the completely incoherent state.
60. Note that the result of the dynamical simulation of the finite-size system is not sensitive to the presence of a small amount of noise, provided we observe phase-locked states and chimera states only. However, the presence of noise is crucial if we want to resolve the stability properties of the completely incoherent state.
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