Subtle escaping modes and subset of patterns from a nonhyperbolic chaotic attractor.

Noise-induced escape from the domain of attraction of a nonhyperbolic chaotic attractor in a periodically excited nonlinear oscillator is further investigated. Deviations are found to be amplified at the primary homoclinic tangency from which the optimal force begins to fluctuate dramatically. Escaping trajectories turn out to possess several modes to pass through the saddle cycle on the basin boundary, and each mode corresponds to a certain type of value of the action plot, respectively. A subset of the pattern of fluctuational paths from the chaotic attractor is obtained, showing the existence of complicated singularities.