Glassy dynamics in arrays of chaotic oscillators

摘要

Arrays of coupled chaotic elements have been used as models for studying a wide range of phenomena such as synchronization and pattern formation in biological and physical systems. We present experimental and numerical results showing that these arrays can also help us understand the origin of the stretched exponential dynamics observed in glasses and other complex systems. Stretched exponential behavior has been measured over many decades in a 1D array of coupled diode-resonators, just above a crisis-induced intermittency transition. Similar results are obtained numerically in an array of identical chaotic oscillators, confirming the chaotic origin of this universal behavior. In these systems, we find that the fundamental physical quantity associated with stretched exponentials is not the auto-correlation function but, rather, the distribution of times spent in dynamical traps. Here, we review these results and discuss their relation with other systems. We will also present results obtained on higher dimensional networks.