메뉴 건너뛰기




Volumn 67, Issue 5, 2006, Pages 629-671

Fourier methods for quasi-periodic oscillations

Author keywords

Averaging method; Fourier method; Invariant torus; Quasi periodic oscillation; Van der Pol oscillator

Indexed keywords

ALGORITHMS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); RELIABILITY;

EID: 33746173012     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1632     Document Type: Article
Times cited : (75)

References (38)
  • 1
    • 0000435339 scopus 로고
    • Quasiperiodically forced damped pendula and Schrödinger equations with quasiperiodic potentials: Implications of their equivalence
    • Bondeson A, Ott E, Antonsen TM. Quasiperiodically forced damped pendula and Schrödinger equations with quasiperiodic potentials: implications of their equivalence. Physical Review Letters 1985; 55:2103-2106.
    • (1985) Physical Review Letters , vol.55 , pp. 2103-2106
    • Bondeson, A.1    Ott, E.2    Antonsen, T.M.3
  • 2
    • 0001725542 scopus 로고
    • Transition from quasiperiodicity to chaos in a Josephson junction analog
    • He DR, Yeh WJ, Kao YH. Transition from quasiperiodicity to chaos in a Josephson junction analog. Physical Reveiw B 1984; 30:172-178.
    • (1984) Physical Reveiw B , vol.30 , pp. 172-178
    • He, D.R.1    Yeh, W.J.2    Kao, Y.H.3
  • 3
    • 0000864550 scopus 로고
    • Quasiperiodic transitions to chaos of instabilities in an electron-hole plasma excited by AC perturbations at one and at two frequencies
    • Held GA, Jeffries C. Quasiperiodic transitions to chaos of instabilities in an electron-hole plasma excited by AC perturbations at one and at two frequencies. Physical Review Letters 1986; 56:1183-1186.
    • (1986) Physical Review Letters , vol.56 , pp. 1183-1186
    • Held, G.A.1    Jeffries, C.2
  • 4
    • 0000009552 scopus 로고
    • Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study
    • Aronson DG, Chory MA, Hall GR, McGehee RP. Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer-assisted study. Communications in Mathematical Physics 1982; 83:303-354.
    • (1982) Communications in Mathematical Physics , vol.83 , pp. 303-354
    • Aronson, D.G.1    Chory, M.A.2    Hall, G.R.3    McGehee, R.P.4
  • 6
    • 0024036863 scopus 로고
    • Quasi-periodicity and dynamical systems: An experimentalists view
    • Glazier JA, Libchaber A. Quasi-periodicity and dynamical systems: an experimentalists view. IEEE Transactions on Circuits and Systems 1988; 35(7):790-809.
    • (1988) IEEE Transactions on Circuits and Systems , vol.35 , Issue.7 , pp. 790-809
    • Glazier, J.A.1    Libchaber, A.2
  • 8
    • 0000882178 scopus 로고    scopus 로고
    • A tutorial on KAM theory. Smooth ergodic theory and its applications (Seattle, WA, 1999)
    • American Mathematical Society: Providence, RI
    • De la Llave R. A tutorial on KAM theory. Smooth ergodic theory and its applications (Seattle, WA, 1999). Proceedings of Symposia in Pure Mathematics, vol. 69. American Mathematical Society: Providence, RI, 2001; 175-292.
    • (2001) Proceedings of Symposia in Pure Mathematics , vol.69 , pp. 175-292
    • De la Llave, R.1
  • 17
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • translated from Prikladnaya Matematika I Mekhanika 1984; 48(2):197-204 (Russian)
    • Neishtadt AI. The separation of motions in systems with rapidly rotating phase. Journal of Applied Mathematics and Mechanics 1985; 48(2):133-139; translated from Prikladnaya Matematika I Mekhanika 1984; 48(2):197-204 (Russian).
    • (1985) Journal of Applied Mathematics and Mechanics , vol.48 , Issue.2 , pp. 133-139
    • Neishtadt, A.I.1
  • 23
  • 24
    • 33746114480 scopus 로고    scopus 로고
    • TorCont: Computation and continuation of quasi-periodic invariant tori
    • Software package
    • Schilder F. TorCont: computation and continuation of quasi-periodic invariant tori. Software package, http://www.dynamicalsystems.org/sw/sw/ detail?item=44
    • Schilder, F.1
  • 26
    • 33644892636 scopus 로고
    • Quasi-periodic oscillations in non-linear control systems
    • Nippon Printing and Publishing Company, Ltd.: Yoshino, Fukushima-ku, Osaka, Japan
    • Hayashi C. Quasi-periodic oscillations in non-linear control systems. Selected Papers on Nonlinear Oscillations. Nippon Printing and Publishing Company, Ltd.: Yoshino, Fukushima-ku, Osaka, Japan, 1975.
    • (1975) Selected Papers on Nonlinear Oscillations
    • Hayashi, C.1
  • 27
    • 0003706768 scopus 로고
    • Lecture Notes in Mathematics, Springer: Berlin, New York
    • Hirsch MW, Pugh CC, Shub M. Invariant Manifolds. Lecture Notes in Mathematics, vol. 583. Springer: Berlin, New York, 1977.
    • (1977) Invariant Manifolds , vol.583
    • Hirsch, M.W.1    Pugh, C.C.2    Shub, M.3
  • 28
    • 33746114479 scopus 로고
    • Resonance phenomena for two-parameter families of maps of the plane: Uniqueness and nonuniqueness of rotation numbers
    • Interaction Mechanics and Mathematical Series. Pitman: Boston, MA
    • Aronson DG, Chory MA, Hall GR, McGehee RP. Resonance phenomena for two-parameter families of maps of the plane: uniqueness and nonuniqueness of rotation numbers. Nonlinear Dynamics and Turbulence. Interaction Mechanics and Mathematical Series. Pitman: Boston, MA, 1983; 35-47.
    • (1983) Nonlinear Dynamics and Turbulence , pp. 35-47
    • Aronson, D.G.1    Chory, M.A.2    Hall, G.R.3    McGehee, R.P.4
  • 29
    • 0004097141 scopus 로고
    • Bifurcations and chaotic state in forced oscillatory circuits containing saturable inductors
    • Carroll T, Pecora L (eds). World Scientific Publishing: Singapore
    • Yoshinaga T, Kawakami H. Bifurcations and chaotic state in forced oscillatory circuits containing saturable inductors. In Nonlinear Dynamics in Circuits, Carroll T, Pecora L (eds). World Scientific Publishing: Singapore, 1995; 89-118.
    • (1995) Nonlinear Dynamics in Circuits , pp. 89-118
    • Yoshinaga, T.1    Kawakami, H.2
  • 30
    • 0003957368 scopus 로고
    • McGraw-Hill: New York, 1964; Princeton University Press: Princeton, NJ
    • Hayashi C. Nonlinear Oscillations in Physical Systems. McGraw-Hill: New York, 1964; Princeton University Press: Princeton, NJ, 1986.
    • (1986) Nonlinear Oscillations in Physical Systems
    • Hayashi, C.1
  • 33
    • 0040845842 scopus 로고    scopus 로고
    • On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem
    • Castellà E, Jorba À. On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics 2000; 76(1):35-54.
    • (2000) Celestial Mechanics , vol.76 , Issue.1 , pp. 35-54
    • Castellà, E.1    Jorba, À.2
  • 34
    • 0040483472 scopus 로고    scopus 로고
    • Numerical computation of the normal behaviour of invariant curves of n-dimensional maps
    • Jorba À. Numerical computation of the normal behaviour of invariant curves of n-dimensional maps. Nonlinearity 2001; 14(5):943-976.
    • (2001) Nonlinearity , vol.14 , Issue.5 , pp. 943-976
    • Jorba, À.1
  • 35
    • 33644905991 scopus 로고    scopus 로고
    • Numerische Approximation quasiperiodischer invarianter Tori unter Anwendung erweiterter Systeme
    • Dissertation, elektronische Veröffentlichung unter TU Ilmenau
    • Schilder F. Numerische Approximation quasiperiodischer invarianter Tori unter Anwendung erweiterter Systeme. Dissertation, elektronische Veröffentlichung unter http://www.db-thueringen.de/servlets/ DocumentServlet?id=2058, TU Ilmenau, 2004.
    • (2004)
    • Schilder, F.1
  • 36
    • 0019621171 scopus 로고
    • Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies
    • Chua LO, Ushida A. Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies. IEEE Transactions on Circuits and Systems 1981; 28(10):953-971.
    • (1981) IEEE Transactions on Circuits and Systems , vol.28 , Issue.10 , pp. 953-971
    • Chua, L.O.1    Ushida, A.2
  • 37
    • 0032024535 scopus 로고    scopus 로고
    • Construction of invariant torus using Toeplitz Jacobian matrices/fast Fourier transform approach
    • Ge T, Leung AYT. Construction of invariant torus using Toeplitz Jacobian matrices/fast Fourier transform approach. Nonlinear Dynamics 1998; 15:283-305.
    • (1998) Nonlinear Dynamics , vol.15 , pp. 283-305
    • Ge, T.1    Leung, A.Y.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.