Spiral Waves in Chaotic Systems

Destruction of spiral waves in chaotic media.

Spiral-wave breakup in strongly chaotic media with nonphase-coherent chaotic attractors is investigated. Spiral-wave dynamics is studied for the Rössler reaction diffusion equation as the local attractor changes from a phase-coherent to a funnel form. Stable spiral waves with an Archimedean structure are observed to persist even when the local chaotic attractor has a funnel form. The destructio...

Structure of complex-periodic and chaotic media with spiral waves.

Spiral wave chimeras in complex oscillatory and chaotic systems.

We demonstrate for the first time that spiral wave chimeras-spiral waves with spatially extended unsynchronzied cores-can exist in complex oscillatory and even locally chaotic homogeneous systems under nonlocal coupling. Using ideas from phase synchronization, we show in particular that the unsynchronized cores exhibit a distribution of different frequencies, thus generalizing the main concept ...

Bifurcation to spiral waves in reaction-di usion systems

For a large class of reaction-diiusion systems on the plane, we show rigorously that typically m-armed spiral waves bifurcate from a homogeneous equilibrium when the latter undergoes a Hopf bifurcation. In particular, we construct a nite-dimensional manifold which contains the set of small rotating waves close to the homogeneous equilibrium. Examining the ow on this center-manifold in a very ge...

Bifurcation to Spiral Waves in Reaction-diffusion Systems

For a large class of reaction-diiusion systems on the plane, we show rigorously that m-armed spiral waves bifurcate from a homogeneous equilibrium when the latter undergoes a Hopf bifurcation. In particular, we construct a nite-dimensional manifold which contains the set of small rotating waves close to the homogeneous equilibrium. Examining the ow on this center-manifold in a very general exam...