Published January 27, 2023 | Version v1
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Chaotic intermittency with non-differentiable M(x) function

  • 1. Universidad de Córdoba
  • 2. Universidad Politécnica de Madrid
  • 3. ROR icon Consejo Nacional de Investigaciones Científicas y Técnicas

Description

One-dimensional maps showing chaotic intermittency with discontinuous reinjection probability density functions are studied. For these maps, the reinjection mechanism possesses two different processes. The M function methodology is applied to analyze the complete reinjection mechanism and to determine the discontinuous reinjection probability density function. In these maps, the function M(x) is continuous and non-differentiable. Theoretical equations are found for the function M(x) and for the reinjection probability density function. Finally, the theoretical results are compared with numerical data finding high accuracy.

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Dates

Available
2023-01-27

References

  • S. Elaskar and E. Del Río, New advances on chaotic intermittency and its applications. Springer, 2017.
  • H. G. Schuster and W. Just, Deterministic chaos. John Wiley & Sons, 2005.
  • A. H. Nayfeh and B. Balachandran, Applied nonlinear dynamics. John Wiley & Sons, 1995.
  • G. Pizza, C. E. Frouzakis, and J. Mantzaras, "Chaotic dynamics in premixed hydrogen/air channel flow combustion," Combustion Theory and Modelling, vol. 16, no. 2, pp. 275–299, 2012.
  • P. De Anna, T. Le Borgne, M. Dentz, A. M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Physical review letters, vol. 110, no. 18, p. 184502, 2013.
  • C. Stan, C. Cristescu, and D. Dimitriu, "Analysis of the intermittent behavior in a low-temperature discharge plasma by recurrence plot quantification," Physics of Plasmas, vol. 17, no. 4, p. 042115, 2010.
  • A. Chian, Complex systems approach to economic dynamics. Springer Science & Business Media, 2007.
  • J. Żebrowski and R. Baranowski, "Type i intermittency in nonstationary systems—models and human heart rate variability," Physica A: Statistical Mechanics and Its Applications, vol. 336, no. 1-2, pp. 74–83, 2004.
  • P. Paradisi, P. Allegrini, A. Gemignani, M. Laurino, D. Menicucci,and A. Piarulli, "Scaling and intermittency of brain events as a manifestation of consciousness," in AIP Conference Proceedings, vol. 1510, no. 1. American Institute of Physics, 2013, pp. 151–161.
  • J. Bragard, J. Vélez, J. Riquelme, L. Pérez, R. Hernández-García, R. Barrientos, and D. Laroze, "Study of type-iii intermittency in the landau–lifshitz-gilbert equation," Physica Scripta, vol. 96, no. 12, p.124045, 2021.
  • P. Ge and H. Cao, "Intermittent evolution routes to the periodic or the chaotic orbits in rulkov map," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 31, no. 9, p. 093119, 2021.
  • I. Belyaev, D. Biryukov, D. N. Gerasimov, and E. Yurin, "On-off intermittency and hard turbulence in the flow of fluid in the magnetic field," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 8, p. 083119, 2019.
  • P. Bordbar and S. Ahadpour, "Type-i intermittency from Markov binary block visibility graph perspective," Journal of Applied Statistics, vol. 48, no. 7, pp. 1303–1318, 2021.
  • L.-W. Kong, H. Fan, C. Grebogi, and Y.-C. Lai, "Emergence of transient chaos and intermittency in machine learning," Journal of Physics: Complexity, vol. 2, no. 3, p. 035014, 2021.
  • S. G. Stavrinides, A. N. Miliou, T. Laopoulos, and A. Anagnostopoulos, "The intermittency route to chaos of an electronic digital oscillator," International Journal of Bifurcation and Chaos, vol. 18, no. 05, pp.1561–1566, 2008.
  • S. Zambrano, I. P. Mariño, and M. A. Sanjuán, "Controlling crisis-induced intermittency using its relation with a boundary crisis," New Journal of Physics, vol. 11, no. 2, p. 023025, 2009.
  • P. Manneville and Y. Pomeau, "Intermittency and the lorenz model," Physics Letters A, vol. 75, no. 1-2, pp. 1–2, 1979.
  • M. Bauer, S. Habip, D.-R. He, and W. Martienssen, "New type of intermittency in discontinuous maps," Physical review letters, vol. 68, no. 11, p. 1625, 1992.
  • D.-R. He, M. Bauer, S. Habip, U. Krueger, W. Martienssen, B. Christiansen, and B.-H. Wang, "Type v intermittency," Physics Letters A, vol. 171, no. 1-2, pp. 61–65, 1992.
  • J. Fan, F. Ji, S. Guan, B.-H. Wang, and D.-R. He, "The distribution of laminar lengths in type v intermittency," Physics Letters A, vol. 182, no. 2-3, pp. 232–237, 1993.
  • T. Price and T. Mullin, "An experimental observation of a new type of intermittency," Physica D: Nonlinear Phenomena, vol. 48, no. 1, pp. 29–52, 1991.
  • N. Platt, E. Spiegel, and C. Tresser, "On-off intermittency: A mechanism for bursting," Physical Review Letters, vol. 70, no. 3, p. 279, 1993.
  • J. Heagy, N. Platt, and S. Hammel, "Characterization of on-off intermittency," Physical Review E, vol. 49, no. 2, p. 1140, 1994.
  • A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, "Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization," Physical review letters, vol. 79, no. 1, p. 47, 1997.
  • A. Pikovsky, M. Rosenblum, and J. Kurths, "Synchronization: a universal concept in nonlinear science," 2002.
  • M. Kurovskaya, "Distribution of laminar phases at eyelet-type intermittency," Technical Physics Letters, vol. 34, no. 12, pp. 1063–1065, 2008.
  • A. E. Hramov, A. A. Koronovskii, M. K. Kurovskaya, and S. Boccaletti, "Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization," Physical review letters, vol. 97, no. 11, p. 114101, 2006.
  • J. Hirsch, B. Huberman, and D. Scalapino, "Theory of intermittency," Physical Review A, vol. 25, no. 1, p. 519, 1982.
  • S. Elaskar, E. Del Rio, and J. M. Donoso, "Reinjection probability density in type-iii intermittency," Physica A: Statistical Mechanics and its Applications, vol. 390, no. 15, pp. 2759–2768, 2011.
  • E. del Rio, S. Elaskar, and V. A. Makarov, "Theory of intermittency applied to classical pathological cases," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 23, no. 3, p. 033112, 2013.
  • E. del Rio, S. Elaskar, and J. M. Donoso, "Laminar length and characteristic relation in type-i intermittency," Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 4, pp. 967–976, 2014.
  • G. Krause, S. Elaskar, and E. del Río, "Noise effect on statistical properties of type-i intermittency," Physica A: Statistical Mechanics and its Applications, vol. 402, pp. 318–329, 2014.
  • S. Elaskar, E. del Rio, G. Krause, and A. Costa, "Effect of the lower boundary of reinjection and noise in type-ii intermittency," Nonlinear Dynamics, vol. 79, no. 2, pp. 1411–1424, 2015.
  • S. Elaskar and E. Del Río, "Discontinuous reinjection probability density functions in type v intermittency," Journal of Computational and Nonlinear Dynamics, vol. 13, no. 12, p. 121001, 2018.
  • S. Elaskar, E. Del Rio, and A. Costa, "Reinjection probability density for type-iii intermittency with noise and lower boundary of reinjection," Journal of Computational and Nonlinear Dynamics, vol. 12, no. 3, p. 031020, 2017.
  • S. Elaskar, E. del Río, and S. Elaskar, "Intermittency reinjection in the logistic map," Symmetry, vol. 14, no. 3, p. 481, 2022.
  • S. Elaskar, E. del Río, and W. Schulz, "Analysis of the type v intermittency using the perron-frobenius operator," Symmetry, vol. 14, p. 2519, 2022.
  • S. Elaskar, E. del Río, and L. Gutierrez Marcantoni, "Nonuniform reinjection probability density function in type v intermittency," Nonlinear Dynamics, vol. 92, p. 683697, 2018.