In addition, modulated traveling pulses have been observed and analyzed. The conditions of a transition from the well known long range repulsion between pulses in excitable media to a previously unknown long range attraction have been found in numerical simulations and studied employing a two-scale perturbation theory, kinematic theory and numerical stability analysis. Localized, circular spots Here, the instabilities of stationary circular spots are studied in numerical simulations and compared to analytical results derived from perturbation theory. It is shown under which conditions the bifurcation is supercritical and leads to stable moving circular spots. Spiral breakup Spiral breakup has been studied in two-dimensional excitable and oscillatory media.
Breakup occurs for an absolute instability of the wavetrain selected by the spiral or the source.
Wave curvature has been found to enhance the instability in two dimensions. Altogether, we have linked appearance of spiral chaos for the first time to a linear instability of rotating spirals. We have especially that interaction of wave patterns with the Turing structures near the appropriate Codimension-2 point. Far away from onset new patterns such as drifting states of waves inside a stationary pattern and vice versa have been discovered.