Crisis, unstable dimension variability, and bifurcations in a system with high-dimensional phase space: Coupled sine circle maps

摘要

The phenomenon of crisis in systems evolving in high-dimensional phase space can show unexpected andninteresting features. We study this phenomenon in the context of a system of coupled sine circle maps. Wenestablish that the origins of this crisis lie in a tangent bifurcation in high dimensions, and identify the routesnthat lead to the crisis. Interestingly, multiple routes to crisis are seen depending on the initial conditions of thensystem, due to the high dimensionality of the space in which the system evolves. The statistical behavior seennin the phase diagram of the system is also seen to change due to the dynamical phenomenon of crisis, whichnleads to transitions from nonspreading to spreading behavior across an infection line in the phase diagram.nUnstable dimension variability is seen in the neighborhood of the infection line. We characterize this crisis andnunstable dimension variability using dynamical characterizers, such as finite-time Lyapunov exponents and theirndistributions. The phase diagram also contains regimes of spatiotemporal intermittency and spatial intermittency,nwhere the statistical quantities scale as power laws. We discuss the signatures of these regimes in the dynamicncharacterizers, and correlate them with the statistical characterizers and bifurcation behavior. We find that it isnnecessary to look at both types of correlators together to build up an accurate picture of the behavior of the system.