Characterization of dynamical properties and indicators of regime change in intermittent chaotic systems

Intermittency has been initially linked to systems alternating regular and irregular states, while nowadays, it also encompasses systems that switch between two or more regimes. These include geophysical processes such as turbulence, convection, and precipitation patterns, not to mention applications in plasma physics, medicine, neuroscience, and economics. Traditionally, the study of intermittency has focused on global statistical indicators, such as the average frequency of regime changes under fixed conditions, or how these vary as a function of the system’s parameters or forcing, like in the case of climate change. However, these global indicators fail in capturing the local spatio-temporal nature of the regime transitions. 

In this work, we use  global and local perspectives to analyze intermittent systems and uncover reliable indicators of regimes’ changes. In particular, using tools such as the Lyapunov exponents and Covariant Lyapunov Vectors (CLVs), we have been able to characterize both global dynamics and local transitions in five different systems, of various complexities, and for three types of intermittency. We identified some key indicators and precursors of the regime transition that are common, despite the differences in the intermittency mechanism and in the dynamical model properties. At the same time, intermittency-type related mechanisms have been unveiled. For instance, we discover very peculiar behaviors in the Lorenz 96 (L96; Lorenz, 1996) and in the Kuramoto-Shivanshinki models (KS;  Kuramoto, Y. and Tsuzuki, T., 1976; G. Sivashinsky, 1977) that, despite their notoriety, have been so far unseen. In the L96 we identified crisis-induced intermittency with pseudo-periodic intermissions. In the KS equations we detected a spatially global intermittency which follows the scaling of type-I intermittency. 

In our local analysis, we uncover the relation between the CLVs mutual alignment and the regimes’ change, a connection that is present in all of the systems and for all types of intermittency considered. In the case of the on-off intermittency, the angle between CLVs is an effective precursor of the jump to the “on” regime. Furthermore, in all systems, the last CLV (the most stable), was found to carry important information about the dynamical features of the intermittency. In the case of type-I intermittency it allowed us to reconstruct the limit cycle around which the intermittency develops, in merging-crisis type of intermittency the last CLV successfully detected the pseudo-periodic intermissions, while in the case of on-off intermittency it allowed us to indicate the “off” state. 

The identification of these general and fundamental mechanisms driving intermittent behaviours, and in particular the detection of indicators spotting the regimes’ change, have the potential to be impactful in the study of turbulent geophysical fluids, rainfall patterns or atmospheric deep convection. In particular, they could be used to define a latent space of reduced dimension in which a neural network can be trained to automatically predict regime changes.