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

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.