Figure 5
The scaling behavior of the averaged long-term distance d 12(t = 200) (colored circles), see Eq. (2), with the respective fits on a log-log scale (fitted for δ < 10−2) (solid lines, cf. Fig. 3). The distribution of the non-averaged distances \({d}_{12}^{({\rm{l}})}(t=200)\), as obtained from 1000 initial conditions, are shown in addition (gray circles). (a) For PPC with \(\rho ={\rho }_{2}^{\ast }=180.95\) one finds, in agreement with Fig. 3, a close to constant cross-distance scaling. (b) For a laminar flow with ρ = ρ 3 = 181.10 the scaling exponent is ν ≈ 1 for distances δ < 10−2. In both cases the scaling breaks down when a symmetry related close-by attractor starts to attract a fraction of the orbits for δ > 10−2.
