Lyapunov exponents near a crisis in a spin-wave experiment.

Abstract

We have calculated the largest Lyapunov exponent near a crisis in spin-wave excitations in the ferrimagnetic material yttrium iron garnet. When the rf driving power is above the crisis, we observe chaotic transients. When the driving power is below the crisis, the largest Lyapunov exponent follows a scaling law as power is varied. We compare our observations in this high-dimensional system to the period-doubling cascade in one-dimensional maps, and suggest that the scaling law for the Lyapunov exponent might be caused by a high-dimensional inverse cascade.