EXPERIMENTAL CONFIRMATION OF THE NEW THEORY OF NOISY INTERMITTENCY

DEL RIO, EZEQUIEL; ELASKAR, SERGIO

Madrid

Congreso; 15th Experimental Chaos and Complexity Conference; 2018

Universidad Rey Juan Carlos

p { margin-bottom: 0.25cm; direction: ltr; color: rgb(0, 0, 0); line-height: 120%; }p.western { font-family: "Liberation Serif","Times New Roman",serif; font-size: 12pt; }p.cjk { font-family: "WenQuanYi Micro Hei"; font-size: 12pt; }p.ctl { font-family: "Lohit Devanagari"; font-size: 12pt; }Intermittencyis a specific route to the deterministic chaos when spontaneoustransitions between laminar and chaotic dynamics occur. It wasintroduced by Pomeau and Maneville {1,2,3}. Later it has been foundthat transition to chaos through intermittency occurs in manyphenomena.Themain attribute of intermittency is the reinjection mechanism thatmaps trajectories of the system from the chaotic region into thelocal laminar phase. This mechanism can be described by thecorresponding reinjection probability density (RPD).Asanalytical expressions for the RPD are available for a few problemsonly, the most common approximation used to obtain many classicalresults on intermittency theory have been considered the RPD uniform{3,4}.Recentlya generalization of the classical intermittency theory has beenpresented, where new methods to investigate the RPD in systemsshowing Type-I, II, or III intermittency are offered. The classicaltheory is included in this new framework as a particular case {5}.The new theory has not been checked on continuous experimentalsystems.Wepresent an experimental system based on an analog electronic circuit.The experimental results are in good agreement with the new theory.Noisehas strong impact on the intermittency phenomena. The generalized RPDintroduces a novel scenario. Whereas the uniform reinjection shouldremain constant under a wide class of noise, the new one is affectedby the noise.Recentlyan analytical approach to the noisy reinjection probability densityhas been presented {6}.We are also focusing on the role of thenoise in our experiment and we have found good agreement with the newnoisy intermittency approachment.The(signal)/(internal noise) relation can be turned in the circuit. Thisfact is used to investigate the noise effect by using the naturalnoise in the circuit, without any external noise generator.It isalso important to note that a complete description of the idealnoiseless system and the real noisy experiment can be obtained fromexperimental noisy data.Thiswork was supported by the former Spanish Ministry of Science andInnovation (ESP2013-41078-R), by CONICET, National University ofCórdoba, MCyT of Córdoba and Universidad Politécnica de Madrid.References1 - Manneville, P. \& Pomeau, Y. [1979]``Intermittency and the Lorenz model,'' Phys. Lett. A, 75, p.1.2 - Pomeau, Y. and Manneville, P. [1980] `` intermittent transitionto turbulence in dissipative dynamical systems,'' Commun. in Math.Phys. 74, 189?197.3 - Manneville, P.[1980] ``Intermittency, self-similarity and 1/fspectrum in dissipative dynamical systems'', Le Journal de Physique,41, 1235?1243.4 - Schuste, H. and Just, W. [2005] Deterministic Chaos. AnIntroduction, WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim, Germany.5 - Elaskar, S. and del Rio E. [2016], New Advances on ChaoticIntermittency and Applications, Springer International Publishing AG,Cham6 - del Rio, E., Sanjuán, M.A.F. and Elaskar, S. [2012] ``Effect ofnoise on the reinjection probability density in intermittency'',Commun. Nonlinear Sci. Numer. Simulat. 17, 3587-3596.