ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


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Slipushenko S. V., Tur A. V., Yanovsky V. V. Intermittency concurrence. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 3-19. DOI: 10.18500/0869-6632-2008-16-4-3-19

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Russian
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Article
UDC: 
514.8; 517.938; 530.182

Intermittency concurrence

Autors: 
Slipushenko Sergej Vasilevich, Institute of Monocrystals of NAS of Ukraine
Tur Anatolij Valentinovich, Institut de Recherche en Astrophysique et Planetologie
Yanovsky Vladimir Vladimirovich, Institute of Monocrystals of NAS of Ukraine
Abstract: 

In this paper we studied intermittent modes in the two-parametric set of onedimensional maps with the neutral unstable point at a phase space boundary. We built the phase diagram in a space of parameters. It defines possible transitions to chaos with a parameter change. We showed the unusual mode of the intermittency concurrence. We studied the laminar length distribution function, Lyapunov exponent and topological entropy of this maps set.

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Reference: 
  1. Manneville P, Pomeau Y. Intermittency and Lorentz model. Phys. Lett. A. 1979;75(1–2):1–2. DOI: 10.1016/0375-9601(79)90255-X.
  2. Schuster G. Deterministic Chaos. Wiley; 1995. 320 p.
  3. Arnold VI. Geometrical Methods in the Theory of Ordinary Differential Equations. New York: Springer; 1988. 351 p. DOI: 10.1007/978-1-4612-1037-5.
  4. Naydenov SV, Tur AV, Yanovsky AV, Yanovsky VV. New scenario to chaos transition in the mappings with discontinuities. Phys. Lett. A. 2003;320(2–3):160–168. DOI: 10.1016/j.physleta.2003.11.007.
  5. Bauer M, Habip S, He DR, and Martienssen W. New type of intermittency in discontinuous maps. Phys. Rev. Lett. 1992;68(11):1625–1628. DOI: 10.1103/PhysRevLett.68.1625.
  6. Hugo LD, de Cavalcante S, and Rios Leite JR. Logarithmic periodicities in the bifurcations of type-I intermittent chaos. Phys. Rev. Lett. 2004;92(25):254102. DOI: 10.1103/PhysRevLett.92.254102.
  7. May RM. Simple mathematical models with very complicated dynamics. Nature. 1976;261(5560):459–467. DOI: 10.1038/261459a0.
  8. Neimark YI, Landa PS. Stochastic and Chaotic Oscillations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  9. Ben-Mizrache A, Procaccia I, Rosenberg N, Schmidt A, Schuster HG. Real and apparent divergencies in low-frequency spectra of nonlinear dynamical systems. Phys. Rev. A. 1985;31(3):1830–1840. DOI: 10.1103/physreva.31.1830.
  10. Berge P, Pomeau I, Vidal K, Ruelle D, Tuckerman LS. Order within chaos: towards a deterministic approach to turbulence. New York: Wiley; 1984. 329 p.
  11. Zolotarev VM. One-Dimensional Stable Distributions. Mathematical Monograph. Vol. 65. American Mathematical Society, Providence, RI; 1986. 284 p.
  12. Kuznetsov SP. Deterministic Chaos. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  13. Sinai Ya.G. Stochasticity of smooth dynamical systems. Elements of KAM theory. In: Modern Problems of Mathematics. Fundamental Directions. Vol. 2. Dynamical Systems – 2. Moscow: All-Russian Institute of Scientific and Technical Information; 1985. P. 115–122 (in Russian).
  14. Zaslavsky GM, Edelman M. Weak mixing and anomalous kinetics along filamented surfaces. Chaos. 2001;11(2):295–305. DOI: 10.1063/1.1355358.
  15. Casati G, Prosen T. Mixing property of triangular billiards. Phys. Rev. Lett. 1999;83(23):4729–4732. DOI: 10.1103/PhysRevLett.83.4729.
  16. Collet P, Crutchfield JP, Eckmann JP. Computing the topological entropy of maps. Commun. Math. Phys. 1983;88(2):257–262. DOI: 10.1007/BF01209479.
  17. Bolotin YL, Tur AV, Yanovskiy VV. Constructive Chaos. Kharkiv: Institute of Single Crystals; 2005. 420 p. (in Russian).
Received: 
25.06.2007
Accepted: 
10.06.2008
Published: 
31.10.2008
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