Spatio-temporal dynamics of complex-periodic and chaotic systems

grantor: University of TorontoIn this thesis we present a study of the spatial-temporal organization of spatially-distributed media with complex-periodic and chaotic dynamics. In particular we consider systems whose spatially inhomogeneous dynamics exhibits period-doubling bifurcations. The most important feature of these media is the presence of synchronization line defects across which the phase of the local oscillation changes by multiples of 2[pi]. Such line defects are shown to be necessary for the existence of spiral waves in complex-periodic media and all possible types of defect lines are classified for system with local period-2'n' oscillatory dynamics. The transition from complex-periodic to chaotic dynamics is considered in detail. Turbulent regimes characterized by spontaneous nucleation, proliferation and collision of defect lines are described. It is shown that transitions to line-defect turbulence are non-equilibrium phase transitions. Synchronization line defects are identified in systems with excitable dynamics. The formation of spiral waves broken by the presence of defect lines is shown for a prototypical system with super-normal excitability. The discussion of a recent experiment where such spirals were observed in the Belousov-Zhabotinsky reaction system is presented. Due to their general nature, the phenomena presented in this thesis are predicted to be observable in a wide range of spatially distributed systems.Ph.D