Spiral chirality transition and tip splitting in oscillatory media with nonlocal couplings

Abstract

The dynamic behavior of spirals and the spatiotemporal organization in nonlocally coupled oscillatory media are explored in terms of the coupled complex Ginzburg-Landau equations. Chirality transition and tip splitting of spiral wave are found. Both the dispersion relation analysis and numerical simulations reveal that the spiral chirality transition corresponds to a change of the sign of the wave number. Moreover, the underlying mechanism of spiral tip splitting is found to originate from the competition between the local and the nonlocal couplings. The tip splitting behavior and the near-core breakup of spiral wave are found to agree with experimental observations in Belousov-Zhabotinsky reactions.

Chiralities of spiral waves and their transitions

“…We can see from Table III that, after the spiral transition, the curl direction is changed from C = +1 to C = −1, and the rotation direction stays the same, which is similar to that in Ref. [27] [see the spiral transition from Figs. 3(a) to 3(c) in Ref.…”

“…With suitable parameters, we can get the similar transition for spiral waves and their evolution properties as discussed in Ref. [27] (see Fig. 8).…”

“…As a case in point, we would like to study the CCGLE, one investigated in Ref. [27] recently. With suitable parameters, we can get the similar transition for spiral waves and their evolution properties as discussed in Ref.…”

“…3(a) to 3(c) in Ref. [27]]. Equations (5) and 7still work effectively because the propagation direction has been changed from P = +1 to P = −1 at the same time.…”

“…[26] illustrated that, during spiral transitions in the CGLE, the curl direction is conserved, but the rotation one is not conserved any more, while, the study in Ref. [27] showed that the curl direction is no longer conserved in the coupled CGLE (CCGLE) during spiral transitions, and the rotation one is still conserved in such processes. Now some natural problems are, more generally, whether the chiralities are still conserved, whether the topological charge is still conserved, and what are the essential relationships between the chiralities and the topological charges, especially, between the chiralities themselves?…”