Abstract
The classical theory of intermittency assumes in most of the cases uniform density of points reinjected from the chaotic to laminar region as has been explained in Chap. 1 Though it works fine in some model systems, a number of the so-called pathological cases exist, and they are characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. In this chapter we apply the result explained in Chap. 5 to different dynamical systems exhibiting anomalous type-I, type-II, and type-III intermittencies. We have chosen several cases from the literature looking for a wide class of RPDs, including numerical and experimental publications. All of the cases are now included in the framework explained in Chap. 5.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Laugesen, J., Carlsson, N., Mosekilde, E., Bountis, T.: Anomalous statistics for type-III intermittency. Open. Syst. Inf. Dyn. 4, 393–405 (1997)
Pikovsky, A.: A new type of intermittent transition to chaos. J. Phys. A 16, L109–L112 (1983)
Kwon, O., Kim, C., Lee, E., Lee, H.: Effects of reinjection on the scaling property of intermittency. Phys. Rev. E 53, 1253–1256 (1996)
del Rio, E., Elaskar, S., Makarov, S.: Theory of intermittency applied to classical pathological cases. Chaos 23, 033112 (2013)
Elaskar, S., del Rio, E., Donoso, J.: Reinjection probability density in type-III intermittency. Physica A 390, 2759–2768 (2011)
del Rio, E., Velarde, M., Rodríguez-Lozano, A.: Long time data series and difficulties with the characterization of chaotic attractors: a case with intermittency III. Chaos Solitons Fractals 4, 2169–2179 (1994)
Dubois, M., Rubio, M., Berge, P.: Experimental evidence of intermittencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 51, 1446–1449 (1983)
del Rio, E., Elaskar, S.: On the theory of intermittency in 1D maps. Int. J. Bifurcation Chaos 26, 1650228–11 (2016)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Elaskar, S., del Río, E. (2017). Application of the New Formulation to Pathological Cases. In: New Advances on Chaotic Intermittency and its Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-47837-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-47837-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47836-4
Online ISBN: 978-3-319-47837-1
eBook Packages: EngineeringEngineering (R0)