Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 3, Page 1946-1965, September 2024.
Abstract.We study the stability properties and the long-term dynamics of chimeras in systems of globally coupled maps. In particular, we establish a formula for the transverse Lyapunov exponent of the states of the system containing synchronized units. We use this formula to present numerical evidence of attracting chimeras having chaotic dynamics as well as periodic behaviors. We also show that, at least for polynomial local maps, attracting periodic cycles tend to belong to cluster spaces, and, more generally, limit sets of chimera orbits have zero Lebesgue measure for strong coupling regimes.