(a) Phase snapshot of a chimera state in system (1); (b) corresponding time averaged phase velocities . Parameters: N = 200, r = 0.7, and .
(Color) Lyapunov spectra computed for chimera trajectories of (1) with coupling radius r = 0.63 (red circles), 0.69 (green diamonds), and 0.73 (blue triangles), and phase lag .
(Color) Dependence of the maximal Lyapunov exponent on the coupling radius r and the phase lag . The gray region at the bottom indicates the parameter region, where we found chimera trajectories for N = 100, the green line indicates the boundary of the existence region for chimera states in the thermodynamic limit .
Relative Lyapunov dimension (dots) and relative size of the incoherent region S incoh (solid line): (a) for varying coupling radius r, and , (b) for varying system size N, and r = 0.7, .
(Color) Lyapunov spectra computed for chimera trajectories of (1) with system size N = 60 (red circles), 90 (green diamonds), and 120 (blue triangles). Other parameters: r = 0.7, .
Scaling behavior of the maximal Lyapunov exponent and of the intermediate Lyapunov exponent . (a) Natural and (b) logarithmic scale. Fitted lines and . Parameters: r = 0.7, .
Solutions of self-consistency Eqs. (13) and (14). (a) Local mean field , (b) corresponding nonlocal coupling force . Parameters: r = 0.7, .
(a) Continuous spectrum of a chimera state in system Eq. (1) with r = 0.7 and . (b) Corresponding Lyapunov spectrum function according to Eq. (20).
(Color) Comparison of the Lyapunov spectra (color dots) from Fig. 2 with the corresponding Lyapunov spectrum functions (color lines) defined by Eq. (20).
Article metrics loading...
Full text loading...