Effect of noise on the neutral direction of chaotic attractor.
A chaotic attractor from a deterministic flow must necessarily possess a neutral direction, as characterized by a null Lyapunov exponent. We show that for a wide class of chaotic attractors, particularly those having multiple scrolls in the phase space, the existence of the neutral direction can be extremely fragile in the sense that it is typically destroyed by noise of arbitrarily small amplitude. A universal scaling law quantifying the increase of the Lyapunov exponent with noise is obtained. A way to observe the scaling law in experiments is suggested.
Department of Mathematics and Statistics, and Departments of Electrical Engineering and Physics, Arizona State University, Tempe, Arizona 85287, USA. yclai@chaos1.1a.asu.edu
Ying-Cheng
YC
Lai
Zonghua
Z
Liu
D000465:Algorithms; D003198:Computer Simulation; D004735:Energy Transfer; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes