Exponential Transient Rotating Waves and their Bifurcations in a Ring of Unidirectionally Coupled Bistable Lorenz Systems

Rotating waves in a ring of unidirectionally coupled Lorenz systems are studied. When a single system is bistable and nonchaotic, various rotating waves are generated and bifurcated in the ring of systems. We consider two kinds of rotating waves: exponential transient rotating waves and chaotic rotating waves. Exponential transient rotating waves are those the duration of which increases exponentially with the number of systems in the ring. Chaotic rotating waves are caused through interactions between periodic rotating waves of multiple wave numbers.