Chaotic 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 from the chaotic region into the laminar one. The RPD classically was taken as a constant. This hypothesis is behind the classically reported characteristic relations, a tool describing how the mean value of the laminar length goes to infinity as the control parameter goes to zero. Recently, a generalized non-uniform RPD has been observed in a wide class of 1D maps; hence, the intermittency theory has been generalized. Consequently, the characteristic relations were also generalized. However, the RPD and the characteristic relations observed in some experimental Poincaré maps still cannot be well explained in the actual intermittency framework. We extend the previous analytical results to deal with the mentioned class of maps. We found that in the mentioned maps, there is not a well-defined RPD in the sense that its shape drastically changes depending on a small variation of the parameter of the map. Consequently, the characteristic relation classically associated to every type of intermittency is not well defined and, in general, cannot be determined experimentally. We illustrate the results with a 1D map and we develop the analytical expressions for every RPD and its characteristic relations. Moreover, we found a characteristic relation going to a constant value, instead of increasing to infinity. We found a good agreement with the numerical simulation.
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April 2021
Research Article|
April 19 2021
Type III intermittency without characteristic relation
Special Collection:
Recent Advances in Modeling Complex Systems: Theory and Applications
Ezequiel del Rio
;
Ezequiel del Rio
a)
1
Department of Applied Physics, ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid
, Cardenal Cisneros 3, 28040 Madrid, Spain
a)Author to whom correspondence should be addressed: ezequiel.delrio@upm.es
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Sergio Elaskar
Sergio Elaskar
b)
2
Department of Aeronautics, Facultad de Ciencias Exactas, Físicas y Naturales and Instituto de Estudios Avanzados en Ingeniería y Tecnología (IDIT), Universidad Nacional de Córdoba and CONICET, Av. Velez Sarfield 1611, 5000
Córdoba, Argentina
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a)Author to whom correspondence should be addressed: ezequiel.delrio@upm.es
b)
Electronic mail: selaskar@unc.edu.ar
Note: This paper belongs to the Focus Issue, Recent Advances in Modeling Complex Systems: Theory and Applications.
Chaos 31, 043127 (2021)
Article history
Received:
December 14 2020
Accepted:
April 02 2021
Citation
Ezequiel del Rio, Sergio Elaskar; Type III intermittency without characteristic relation. Chaos 1 April 2021; 31 (4): 043127. https://doi.org/10.1063/5.0040599
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