Transition from outward to inward rotating spiral waves caused by a localized inhomogeneity in the CGLE. (a)–(c) Development of an outward spiral wave from cross-gradient initial condition in the absence of inhomogeneity, i.e., . (d)–(f) The outward spiral is transmitted to an inward spiral after applying the inhomogeneity around the spiral core, . (g) Corresponding space time plot along y = 200 [see dashed lines in (a)] and one finds a clear transition from outward to inward wave propagation. Other parameters are , and . White arrows (the same meaning in Figs. 2 and 5 ) denote the direction of wave propagation, i.e., the phase velocity. The system consists of 400 × 400 grid points. The space and time step is and , respectively.
Transition from inward to outward spirals in Eq. (1) . (a) An inward spiral, ; (b) a frozen spiral, ; (c) an outward spiral, . (d)–(f) are the corresponding space-time plots of (a)–(c). Other parameters are , and .
The dependence of absolute value of the wave number on . (a) and . (b) and . It suggests that the inhomogeneity satisfying leads to the increase of the wave number, while satisfying would decrease the wave number.
The dependence of frequency on . (a) . (b) and . It shows that can change its sign at (see the arrow).
Reversal of spiral waves caused by an obstacle. (a) An outward spiral wave in the CGLE without any obstacle. (b) An inward spiral wave transmitted from (a) caused by an obstacle ( ) around the spiral core. (c) Corresponding space-time plot of the transition from outward to inward rotating spiral wave. (d)–(e) Dependence of the wave number and the frequency on the obstacle “radius” δ. The dependence of (d) and (e) on the obstacle “radius” δ. Here, and .
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