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

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Statistical Physics

Background:

• Nonhyperbolic chaotic attractors are sensitive to initial conditions and external forces.
• Understanding escape dynamics is crucial for predicting system behavior under noise.

Purpose of the Study:

• To investigate noise-induced escape from nonhyperbolic chaotic attractors in periodically excited nonlinear oscillators.
• To analyze the behavior of escaping trajectories and identify patterns in fluctuational paths.

Main Methods:

• Numerical simulations of a periodically excited nonlinear oscillator.
• Analysis of escaping trajectories and their interaction with the basin boundary.
• Examination of the action plot to characterize different escape modes.

Main Results:

• Deviations are amplified at the primary homoclinic tangency, leading to dramatic force fluctuations.
• Escaping trajectories demonstrate multiple modes of passage through the saddle cycle on the basin boundary.
• A subset of fluctuational paths reveals complex singularities originating from the chaotic attractor.

Conclusions:

• Noise-induced escape dynamics are complex and characterized by amplified deviations and multiple trajectory modes.
• The study reveals intricate patterns and singularities in the fluctuational paths of escaping trajectories.
• Findings contribute to a deeper understanding of chaotic system behavior and noise effects.