Metastable and chaotic transient rotating waves in a ring of unidirectionally coupled bistable Lorenz systems

Bifurcations and transients in rings of unidirectionally coupled nonchaotic bistable Lorenz systems were studied. Quasiperiodic and chaotic rotating waves were generated in rings of small numbers of Lorenz systems. Two kinds of exponential transient rotating waves emerged in rings of large numbers of Lorenz systems, the duration of which increased exponentially with the number of Lorenz systems. One was metastable regular rotating waves when a pair of stable steady states and an unstable periodic rotating wave coexisted. The other was chaotic transient rotating waves when multiple periodic rotating waves coexisted. Rings of unidirectionally coupled circle maps were also shown to cause these exponential transient rotating waves.