Experimental Results Versus Computer Simulations of Noisy Poincaré Maps in an Intermittency Scenario

Intermittency is a route to chaos when transitions between laminar and chaotic dynamics occur. The main attribute of intermittency is the reinjection mechanism, described by the reinjection probability density (RPD), which maps trajectories of the system from the chaotic region into the laminar one. The main results on chaotic intermittency strongly depend on the RPD. Recently a generalized power law RPD has been observed in a wide class of 1D maps. Noise has an impact on the intermittency phenomena and the generalized RPD introduces a novel scenario because it is affected by the noise. An analytical approach was introduced to estimate the noisy RPD (NRPD). In this work we investigate the noisy RPD in two cases: an experimental continuous system, by means of a Poincaré map associated to it, and a numerical map chosen close to the experimental one. In the experimental map we use the internal noise of the circuit, whereas in the numerical map we introduce the noise in the usual way.
We have compared both noisy dynamics and found important differences between them, concerning the propagation of the noise effect from the maximum of the map (where the power law is generated) into the laminar region.
To mimic the numerical map by the experiment, we introduced an external noise during a short window of time, obtaining similar results to the ones obtained in the internal natural noise case. We found that our methodology developed to study the noise intermittency can be used to investigate which class of noise is present in continuous systems.