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Volumn 19, Issue 4, 2014, Pages 1027-1034

Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

Author keywords

Chaos; Leonov's conjecture; Lyapunov dimension; Lyapunov exponent; R ssler system; Strange attractor

Indexed keywords

LYAPUNOV METHODS;

EID: 84886303693     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2013.07.026     Document Type: Article
Times cited : (102)

References (38)
  • 1
    • 85196190098 scopus 로고
    • The general problem of the stability of motion. CRC Press
    • Lyapunov AM. The general problem of the stability of motion. CRC Press; 1992.
    • (1992)
    • Lyapunov, A.M.1
  • 2
    • 34250157760 scopus 로고    scopus 로고
    • Time-varying linearization and the Perron effects
    • Leonov G.A., Kuznetsov N.V. Time-varying linearization and the Perron effects. Int J Bifurcation Chaos 2007, 17(4):1079-1107. 10.1142/S0218127407017732.
    • (2007) Int J Bifurcation Chaos , vol.17 , Issue.4 , pp. 1079-1107
    • Leonov, G.A.1    Kuznetsov, N.V.2
  • 3
    • 33744505436 scopus 로고    scopus 로고
    • Criterion of stability to first approximation of nonlinear discrete systems
    • Kuznetsov N.V., Leonov G.A. Criterion of stability to first approximation of nonlinear discrete systems. Vestnik StPetersburg Univ Math 2005, 38(2):52-60.
    • (2005) Vestnik StPetersburg Univ Math , vol.38 , Issue.2 , pp. 52-60
    • Kuznetsov, N.V.1    Leonov, G.A.2
  • 4
    • 85196176662 scopus 로고    scopus 로고
    • Criteria of stability by the first approximation for discrete nonlinear systems
    • Kuznetsov N.V., Leonov G.A. Criteria of stability by the first approximation for discrete nonlinear systems. Vestnik StPetersburg Univ Math 2005, 38(3):21-30.
    • (2005) Vestnik StPetersburg Univ Math , vol.38 , Issue.3 , pp. 21-30
    • Kuznetsov, N.V.1    Leonov, G.A.2
  • 5
    • 33746711700 scopus 로고    scopus 로고
    • On stability by the first approximation for discrete systems. In: 2005 International conference on physics and control, PhysCon
    • Kuznetsov NV, Leonov GA. On stability by the first approximation for discrete systems. In: 2005 International conference on physics and control, PhysCon, vol. 2005; 2005. p. 596-599. doi:10.1109/PHYCON.2005.1514053.
    • (2005) , vol.2005 , pp. 596-599
    • Kuznetsov, N.V.1    Leonov, G.A.2
  • 6
    • 0018989294 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. A method for computing all of them. Part 1: theory
    • Benettin G., Galgani L., Giorgilli A., Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. A method for computing all of them. Part 1: theory. Meccanica 1980, 15(1):9-20.
    • (1980) Meccanica , vol.15 , Issue.1 , pp. 9-20
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 7
    • 0018992908 scopus 로고
    • Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems
    • Benettin G., Galgani L., Giorgilli A., Strelcyn J.M. Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems. Meccanica 1980, 15(1):21-30.
    • (1980) Meccanica , vol.15 , Issue.1 , pp. 21-30
    • Benettin, G.1    Galgani, L.2    Giorgilli, A.3    Strelcyn, J.M.4
  • 8
    • 0000672504 scopus 로고
    • A numerical approach to ergodic problem of dissipative dynamical systems
    • Shimada I., Nagashima T. A numerical approach to ergodic problem of dissipative dynamical systems. Prog Theor Phys 1979, 61(6):1605-1616.
    • (1979) Prog Theor Phys , vol.61 , Issue.6 , pp. 1605-1616
    • Shimada, I.1    Nagashima, T.2
  • 9
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Physica 1985, 16(D):285-317.
    • (1985) Physica , vol.16 , Issue.D , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 11
    • 84863717008 scopus 로고    scopus 로고
    • Lyapunov functions in the attractors dimension theory
    • Leonov G.A. Lyapunov functions in the attractors dimension theory. J Appl Math Mech 2012, 76(2).
    • (2012) J Appl Math Mech , vol.76 , Issue.2
    • Leonov, G.A.1
  • 14
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rossler O.E. An equation for continuous chaos. Phys Lett A 1976, 57(5):397-398.
    • (1976) Phys Lett A , vol.57 , Issue.5 , pp. 397-398
    • Rossler, O.E.1
  • 15
    • 84985456277 scopus 로고
    • Continuous chaos - four prototype equations
    • Rossler O.E. Continuous chaos - four prototype equations. Ann New York Acad Sci 1979, 316(1):376-392.
    • (1979) Ann New York Acad Sci , vol.316 , Issue.1 , pp. 376-392
    • Rossler, O.E.1
  • 16
    • 0001334913 scopus 로고
    • Dimension type characteristics for invariant sets of dynamical systems
    • Pesin Y.B. Dimension type characteristics for invariant sets of dynamical systems. Russ Math Surv 1988, 43:4:111-151. 10.1070/RM1988v043n04ABEH001892.
    • (1988) Russ Math Surv , pp. 111-151
    • Pesin, Y.B.1
  • 19
    • 21944436625 scopus 로고    scopus 로고
    • Lyapunov's direct method in estimates of the fractal dimension of attractors
    • Leonov G.A., Lyashko S.A. Lyapunov's direct method in estimates of the fractal dimension of attractors. Differ Equ 1997, 33(1):67-74.
    • (1997) Differ Equ , vol.33 , Issue.1 , pp. 67-74
    • Leonov, G.A.1    Lyashko, S.A.2
  • 20
    • 0031675003 scopus 로고    scopus 로고
    • The upper estimations for the Hausdorff dimension of attractors
    • Leonov G.A. The upper estimations for the Hausdorff dimension of attractors. Vestnik of the St Petersburg Univ: Math 1998, (1):19-22.
    • (1998) Vestnik of the St Petersburg Univ: Math , Issue.1 , pp. 19-22
    • Leonov, G.A.1
  • 21
    • 21944432516 scopus 로고    scopus 로고
    • Hausdorff and fractal dimension estimates for invariant sets of non-injective maps
    • Boichenko V.A., Leonov G.A., Franz A., Reitmann V. Hausdorff and fractal dimension estimates for invariant sets of non-injective maps. Zeit. Anal. Anwendung 1998, 17(1):207-223.
    • (1998) Zeit. Anal. Anwendung , vol.17 , Issue.1 , pp. 207-223
    • Boichenko, V.A.1    Leonov, G.A.2    Franz, A.3    Reitmann, V.4
  • 22
    • 0034588460 scopus 로고    scopus 로고
    • On estimated for dimension of attractors of the Henon map
    • Boichenko V.A., Leonov G.A. On estimated for dimension of attractors of the Henon map. Vestnik St Petersburg Univ: Math 2000, 33(13):8-13.
    • (2000) Vestnik St Petersburg Univ: Math , vol.33 , Issue.13 , pp. 8-13
    • Boichenko, V.A.1    Leonov, G.A.2
  • 23
    • 80655145029 scopus 로고    scopus 로고
    • Upper estimates for the Hausdorff dimension of negatively invariant sets of local cocycles
    • Leonov G.A., Reitmann V., Slepukhin A.S. Upper estimates for the Hausdorff dimension of negatively invariant sets of local cocycles. Doklady Math 2011, 84(1):551-554. 10.1134/S1064562411050103.
    • (2011) Doklady Math , vol.84 , Issue.1 , pp. 551-554
    • Leonov, G.A.1    Reitmann, V.2    Slepukhin, A.S.3
  • 25
    • 40249108911 scopus 로고    scopus 로고
    • Unstable manifolds for the hyperchaotic Rossler system
    • Szczepaniak A., Macek W.M. Unstable manifolds for the hyperchaotic Rossler system. Phys Lett A 2008, 372(14):2423-2427. 10.1016/j.physleta.2007.12.009.
    • (2008) Phys Lett A , vol.372 , Issue.14 , pp. 2423-2427
    • Szczepaniak, A.1    Macek, W.M.2
  • 26
    • 41349088390 scopus 로고    scopus 로고
    • A topological horseshoe in the hyperchaotic Rossler attractor
    • Li Q. A topological horseshoe in the hyperchaotic Rossler attractor. Phys Lett A 2008, 372(17):2989-2994. 10.1016/j.physleta.2007.11.071.
    • (2008) Phys Lett A , vol.372 , Issue.17 , pp. 2989-2994
    • Li, Q.1
  • 29
    • 0000543733 scopus 로고
    • Multiplicative ergodic theorem: characteristic lyapunov exponents of dynamical systems
    • Oseledec V.I. Multiplicative ergodic theorem: characteristic lyapunov exponents of dynamical systems. Trans Mosc Math Soc 1968, 19:179-210.
    • (1968) Trans Mosc Math Soc , vol.19 , pp. 179-210
    • Oseledec, V.I.1
  • 30
    • 0042963962 scopus 로고    scopus 로고
    • Lattice Boltzmann solver of Rossler equation
    • Yan G., Ruan L. Lattice Boltzmann solver of Rossler equation. Commun Nonlinear Sci Numer Simul 2000, 5(2):64-68. 10.1016/S1007-5704(00)90003-0.
    • (2000) Commun Nonlinear Sci Numer Simul , vol.5 , Issue.2 , pp. 64-68
    • Yan, G.1    Ruan, L.2
  • 31
    • 55549140509 scopus 로고    scopus 로고
    • Application of the differential transformation method for the solution of the hyperchaotic Rossler system
    • Al-Sawalha M.M., Noorani M.S.M. Application of the differential transformation method for the solution of the hyperchaotic Rossler system. Commun Nonlinear Sci Numer Simul 2009, 14(4):1509-1514. 10.1016/j.cnsns.2008.02.002.
    • (2009) Commun Nonlinear Sci Numer Simul , vol.14 , Issue.4 , pp. 1509-1514
    • Al-Sawalha, M.M.1    Noorani, M.S.M.2
  • 32
    • 3042817670 scopus 로고    scopus 로고
    • Difference equations versus differential equations, a possible equivalence for the Rossler system?
    • Letellier C., Elaydi S., Aguirre L.A., Alaoui A. Difference equations versus differential equations, a possible equivalence for the Rossler system?. Physica D: Nonlinear Phenom 2004, 195(1-2):29-49. 10.1016/j.physd.2004.02.007.
    • (2004) Physica D: Nonlinear Phenom , vol.195 , Issue.1-2 , pp. 29-49
    • Letellier, C.1    Elaydi, S.2    Aguirre, L.A.3    Alaoui, A.4
  • 33
    • 67349167672 scopus 로고    scopus 로고
    • Qualitative analysis of the Rossler equations: bifurcations of limit cycles and chaotic attractors
    • Barrio R., Blesa F., Serrano S. Qualitative analysis of the Rossler equations: bifurcations of limit cycles and chaotic attractors. Physica D: Nonlinear Phenom 2009, 238(13):1087-1100. 10.1016/j.physd.2009.03.010.
    • (2009) Physica D: Nonlinear Phenom , vol.238 , Issue.13 , pp. 1087-1100
    • Barrio, R.1    Blesa, F.2    Serrano, S.3
  • 34
    • 80755175875 scopus 로고    scopus 로고
    • Qualitative and numerical analysis of the Rossler model: bifurcations of equilibria
    • Barrio R., Blesa F., Serrano S. Qualitative and numerical analysis of the Rossler model: bifurcations of equilibria. Comput Math Appl 2011, 62(11):4140-4150. 10.1016/j.camwa.2011.09.064.
    • (2011) Comput Math Appl , vol.62 , Issue.11 , pp. 4140-4150
    • Barrio, R.1    Blesa, F.2    Serrano, S.3
  • 35
    • 79956081226 scopus 로고    scopus 로고
    • Localization of hidden Chua's attractors
    • Leonov G.A., Kuznetsov N.V., Vagaitsev V.I. Localization of hidden Chua's attractors. Phys Lett A 2011, 375(23):2230-2233. 10.1016/j.physleta.2011.04.037.
    • (2011) Phys Lett A , vol.375 , Issue.23 , pp. 2230-2233
    • Leonov, G.A.1    Kuznetsov, N.V.2    Vagaitsev, V.I.3
  • 36
    • 80052988208 scopus 로고    scopus 로고
    • Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
    • Bragin V.O., Vagaitsev V.I., Kuznetsov N.V., Leonov G.A. Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits. J Comput Syst Sci Int 2011, 50(4):511-543. 10.1134/S106423071104006X.
    • (2011) J Comput Syst Sci Int , vol.50 , Issue.4 , pp. 511-543
    • Bragin, V.O.1    Vagaitsev, V.I.2    Kuznetsov, N.V.3    Leonov, G.A.4
  • 37
    • 84864278119 scopus 로고    scopus 로고
    • Hidden attractor in smooth Chua systems
    • Leonov G.A., Kuznetsov N.V., Vagaitsev V.I. Hidden attractor in smooth Chua systems. Physica D 2012, 241(18):1482-1486. 10.1016/j.physd.2012.05.016.
    • (2012) Physica D , vol.241 , Issue.18 , pp. 1482-1486
    • Leonov, G.A.1    Kuznetsov, N.V.2    Vagaitsev, V.I.3
  • 38
    • 84874642094 scopus 로고    scopus 로고
    • Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits
    • Article NO: 1330002
    • Leonov G.A., Kuznetsov G.V. Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractors in Chua circuits. Int J Bifurcation Chaos 2013, 23(1):1-69. Article NO: 1330002. 10.1142/S0218127413300024.
    • (2013) Int J Bifurcation Chaos , vol.23 , Issue.1 , pp. 1-69
    • Leonov, G.A.1    Kuznetsov, G.V.2


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