Recent experiments on spiral waves in the Belousov-Zhabotinsky reaction indicate that the waves may break up sufficiently far from the core into chemical turbulence. Simulations of target patterns in the FitzHugh-Nagumo and Ginzburg-Landau models indicate that such transitions occur when the wave frequency pushes the selected wave vector into the regime of absolute Eckhaus instability. This frequency in turn depends on the control parameter and boundary conditions through the solution of a nonlinear eigenvalue problem.

• Received 23 September 1997

DOI:https://doi.org/10.1103/PhysRevLett.80.4811