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All issues Volume 11 / No 2 (2016) Math. Model. Nat. Phenom., 11 2 (2016) 75-88 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016
Spectral problems
Page(s) 75 - 88
DOI https://doi.org/10.1051/mmnp/201611206
Published online 21 March 2016
  1. J. L. Lagrange. Mecanique Analytique. vol. 2, 1788. [Google Scholar]
  2. H. Poincare. Methodes Nouvelles de la Mecanique Celeste. Vol. 3, Gauthier-Villars: Paris, 1899. [Google Scholar]
  3. B. van der Pol. A theory of the amplitude of free and forced triode vibrations. Radio Review 1(1920), 701-710, 754-762. [Google Scholar]
  4. P. Fatou. Sur le mouvement d’un systeme soumis ‘a des forces a courte periode. Bulletin de la Société Mathématique de France. 56(1928), 98-139. [MathSciNet] [Google Scholar]
  5. N.M. Krylov, N.N. Bogolyubov. Methodes approchees de la mecanique nonlineaire dans leurs application a l’Aeetude de la perturbation des mouvements periodiques de divers phenomenes de resonance s’y rapportant. Academie des Sciences d’U-kraine, Kiev(French), 1935. [Google Scholar]
  6. A.C.J. Luo. Continuous Dynamical Systems. HEP/LH Scientific: Beijing/Glen Carbon, 2012. [Google Scholar]
  7. A.C.J. Luo, J.Z. Huang. Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance. Journal of Vibration and Control 18(2012), No. 11, 1661-1871. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.C.J. Luo, J.Z. Huang. Analytical dynamics of period-m flows and chaos in nonlinear systems. International Journal of Bifurcation and Chaos, 22(2012), No. 4, Article No. 1250093 (29 pages). [Google Scholar]
  9. A.C.J. Luo, J.Z. Huang. Analytical routines of period-1 motions to chaos in a periodically forced Duffing oscillator with twin-well potential. Journal of Applied Nonlinear Dynamics, 1(2012), No. 1, 73-108. [CrossRef] [Google Scholar]
  10. A.C.J. Luo, J.Z. Huang. Unstable and stable period-m motions in a twin-well potential Duffing oscillator. Discontinuity Nonlinearity and Complexity 1(2012), No. 3, 113-145. [CrossRef] [Google Scholar]
  11. A.C.J. Luo. Analytical solutions of periodic motions in dynamical systems with/without time-delay. International Journal of Dynamics and Control 1(2013), No. 4, 330-359. [CrossRef] [Google Scholar]
  12. A.C.J. Luo, H.X. Jin. Bifurcation trees of period-m motion to chaos in a Time-delayed, quadratic nonlinear oscillator under a periodic excitation. Discontinuity Nonlinearity and Complexity 3(2014), No. 1, 87-107. [CrossRef] [Google Scholar]
  13. A.C.J. Luo, H.X. Jin. Complex period-1 motions of a periodically forced Duffing oscillator with a time-delay feedback. International Journal of Dynamics and Control, 3(2015), No. 4, 325-340. [CrossRef] [MathSciNet] [Google Scholar]
  14. A.C.J. Luo, A.C.J. Jin. Period-m motions to chaos in a periodically forced Duffing oscillator with a time-delay feedback. International Journal of Bifurcation and Chaos 24(2014), No. 10, Article No.1450126 (20 pages). [Google Scholar]
  15. A.C.J. Luo. The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation. Journal of Sound and Vibration 283(2005), No. 3-5, 723-748. [CrossRef] [Google Scholar]
  16. A.C.J, Luo. Regularity and Complexity in Dynamical Systems. Springer: New York, 2012. [Google Scholar]
  17. A.C.J. Luo. Periodic flows in nonlinear dynamical systems based on discrete implicit maps. International Journal of Bifurcation and Chaos, 25(2015), No. 3, Artical No. 1550044 (62 pages). [Google Scholar]
  18. A.C.J. Luo, Y. Guo. A semi-analytical prediction of periodic motions in Duffing oscillator through mapping structures. Discontinuity Nonlinearity and Complexity, 4 (2015), No. 2, 121-150. [CrossRef] [Google Scholar]

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