Strange periodic attractor: Extremely high stochastic sensitivity of a parametrically modulated system

摘要

Periodical parametric modulation in a chaotic system induces a periodic orbit with a negative global Lyapunov exponent. However, the local Lyapunov exponent takes positive values during certain time intervals in the cycle. The stochastic sensitivity analysis of this strange periodic attractor reveals its extremely high sensitivity to noise. For relatively slow modulation, the stochastic sensitivity function (SSF) reaches the values of 10~(50) in the time intervals where the local Lyapunov exponent is positive, whereas in the region of the negative exponent it is 1. Such extraordinary stochastic sensitivity can be used for creating sensors to detect very small disturbances or noise, based on parametrically modulated chaotic systems with strange periodic attractors.