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Tytuł artykułu

Quasi-Fractional Approximation of Solution to Non-Autonomous Duffing's Equation

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A regular perturbation procedure and quasi-fractional approximants are used for analytical construction of a homoclinic orbit for a Duffing’s equation.
Rocznik
Strony
15--20
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Institut für Allgemeine Mechanik, RWTH Aachen University
  • Department of Automatics and Biomechanics, Technical University of Lodz
Bibliografia
  • 1. Andrianov, I.V., Awrejcewicz, J., 2001, New trends in asymptotic approaches: summation and interpolation methods, Applied Mechanics Review, 54(1), 69-92.
  • 2. Awrejcewicz, J., Andrianov, I.V., Manevitch, L.I., 1998, Asymptotic Approaches in Nonlinear Dynamics: New Trends and Applications, Springer-Verlag, Heidelberg.
  • 3. Drazin, P.G., 1992, Nonlinear Systems, Cambridge University Press.
  • 4. Gelfreich, V.G., Lazutkin, V.F., 2001, Splitting of separatrices perturbation theory and exponential smallness, Russ Math Surveys, 56(3), 499-558.
  • 5. Guckenheimer, J., Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York.
  • 6. Holmes, P., 1980, Averaging and chaotic motions in forced oscillations, SIAM Journal of Applied Mathematics, 38, 65-80.
  • 7. Jordan, D. W., Smith, P., 1999, Nonlinear Ordinary Differential Equations. An Introduction to Dynamical Systems, Oxford University Press.
  • 8. Martin, P, Baker, G.A., 1991, Two-point quasifractional approximant in physics. Truncation error, Journal of Mathematical Physics, 32, 1470-1477.
  • 9. Melnikov, V.K., 1963, On the stability of the center for time periodic perturbations, Transactions of Moscow Mathematical Society, 12, 1-57.
  • 10. Mikhlin, Yu.V., 1985, Joining of local expansion in the nonolinear oscillators theory, Applied Mathematics and Mechanics, 49(5), 738-743.
  • 11. Mikhlin, Yu.V., 1995, Matching of local expansions in the theory of nonlinear vibrations, Journal of Sound and Vibration, 182(4), 5777-588.
  • 12. Mikhlin, Yu. V., 2000, Analytical construction of homoclinic orbits of two-and-three-dimensional dynamical systems, Journal of Sound and Vibration, 230(5), 971-983.
  • 13. Nayfeh, A. H., Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York.
  • 14. Sanders, J.A., 1982, Melnikov' s method and averaging, Celestial Mechanics, 28, 171-181.
  • 15. Smith, P., 1998, The multi scales method, homoclinic bifurcation and Melnikov's method for autonomous system, International Journal of Bifurcation and Chaos, 8, 2099-2105.
  • 16. Smith, P., Yorke, J.M.E., 1992, A dual perturbation series analysis of homoclinic bifurcation for autonomous systems, Zeitschrift für Angewandte Mathematik und Mechanik, 72, 269-275.
  • 17. Vakakis, A.F., 1994, Exponentially small splitting of manifolds in a rapidly forced Duffing system, Journal of Sound and Vibration, 170, 119-129.
  • 18. Vakakis, A.F., Azeez, M.F.A., 1998, Analytic approximation of the homoclinic orbits of the Lorenz system at δ= 10; b = 8/3 and ƿ= 13.926, Nonlinear Dynamics, 15, 245-257.
  • 19. Wiggins, S., 1990, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York.
  • 20. Wiggins, S., Holmes, P., 1987, Homoclinic orbits in slowly varying oscillators, SIAM Journal of Mathematical Analysis, 18, 612-629.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0005-0026
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