Volume 123, Number 4, August 2018
|Number of page(s)||5|
|Published online||12 September 2018|
Strange periodic attractor: Extremely high stochastic sensitivity of a parametrically modulated system
1 Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo 28223 Pozuelo de Alarcón, Madrid, Spain
2 Institute of Mathematics and Computer Sciences, Ural Federal University - Ekaterinburg, Russia
Received: 3 July 2018
Accepted: 22 August 2018
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 1050 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.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 02.50.Fz – Stochastic analysis / 05.40.Ca – Noise
© EPLA, 2018
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