  Independent of specific local features, global spatio-temporal structures in
diverse phenomena around bifurcation points are described by the complex
Ginzburg-Landau equation (CGLE) derived using the reductive perturbation
method, which includes prediction of spatio-temporal chaos. The generality in
the CGLE scheme includes oscillatory instability in slip behavior between
stable and unstable regimes. Such slip transitions accompanying spatio-temporal
chaos is expected for frictional interfaces of a thin elastic layer made of
soft solids, such as rubber or gel, where especially chaotic behavior may be
easily discovered due to their compliance. Slow earthquakes observed in the
aseismic-to-seismogenic transition zone along a subducting plate are also
potential candidates. This article focuses on the common properties of slip
oscillatory instability from the viewpoint of a CGLE approach by introducing a
drastically simplified model of an elastic body with a thin layer, whose local
expression in space and time allows us to employ conventional reduction
methods. Special attention is paid to incorporate a rate-and-state friction law
supported by microscopic mechanisms beyond the Coulomb friction law. We discuss
similarities and discrepancies in the oscillatory instability observed or
predicted in soft matter or a slow earthquake.
