Long Chaotic Transients in Complex Networks

TL;DR

This paper demonstrates that complex networks of pulse-coupled oscillators exhibit long chaotic transients whose durations depend on network connectivity, revealing a new form of robust synchronization and analytical insights into their chaotic behavior.

Contribution

It introduces the phenomenon of long chaotic transients in diluted networks and provides an analytical approximation for their Lyapunov exponents.

Findings

Long chaotic transients dominate network dynamics.

Transient lengths vary with connectivity, peaking at intermediate levels.

A new form of robust synchronization is observed during transients.

Abstract

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The lengths of the transients strongly depend on the network connectivity and varies by several orders of magnitude, with maximum transient lengths at intermediate connectivities. The dynamics of the transient exhibits a novel form of robust synchronization. An approximation to the largest Lyapunov exponent characterizing the chaotic nature of the transient dynamics is calculated analytically.