Transitions to line-defect turbulence in complex oscillatory media

The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes chara cterized by the spontaneous nucleation, proliferation, and erratic motion o f synchronization defect lines which separate domains of different oscillat ion phases. The line-defect dynamics is controlled by the competition betwe en diffusion, which reduces line length and curvature, and phase-gradient-i nduced growth. The onset of each type of defect-line turbulence is identifi ed with a nonequilibrium phase transition characterized by nontrivial criti cal exponents.