494 citations · 2.8k across the 66 of their papers we have counts for
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Transitions to Line-Defect Turbulence in Complex Oscillatory Media
Andrei Goryachev, Hugues Chate', Raymond Kapral
The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nu…
Spiral Waves in Media with Complex Excitable Dynamics
Andrei Goryachev, Raymond Kapral
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown tha…
Perturbation Theory for the Breakdown of Mean-Field Kinetics in Oscillatory Reaction-Diffusion Systems
Mikhail V. Velikanov, Raymond Kapral
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-deat…
Coiling and Supercoiling of Vortex Filaments in Oscillatory Media
Guillaume Rousseau, Hugues Chaté, Raymond Kapral
We study the behavior of vortex filaments subject to a uniform density of phase twist in oscillatory media described by the complex Ginzburg-Landau equation. The first instability…
Synchronization Defects and Broken Symmetry in Spiral Waves
Andrei Goryachev, Hugues Chate, Raymond Kapral
Spiral waves are investigated in oscillatory media exhibiting period-doubling bifurcations. In the period-doubled and chaotic regimes, the rotational symmetry of the spiral wave is…
Slow Manifold Structure and the Emergence of Mixed-Mode Oscillations
Andrei Goryachev, Peter Strizhak, Raymond Kapral
A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase loc…