Bibliography for the Duffing Equation

unabridged

  1. Oscillation-Sliding in a Modified Van Der Pol-Duffing Electronic Oscillator
    A. Algaba, F. Fernandez-Sanchez, E. Freire, E. Gamero, A. J. Rodriguez-Luis  
    Journal of Sound and Vibration, Vol. 249, No. 5, Jan 2002, pp. 899-907, Ideal.  
  2. Advanced feedback control of the chaotic Duffing equation.
    Jiang, Zhong-Ping
    IEEE Trans. Circuits Systems I Fund. Theory Appl. 49 (2002), no. 2, 244--249, MathSciNet.
  3. The Lower Bounds of T-Periodic Solutions for the Forced Duffing Equation
    Chengwen Wang  
    Journal of Mathematical Analysis and Applications, Vol. 260, No. 2, Aug 2001, pp. 507-516, Ideal.  
  4. Boundedness of Solutions for Duffing's Equations with Semilinear Potentials
    Xiong Li  
    Journal of Differential Equations, Vol. 176, No. 1, Oct 2001, pp. 248-268, Ideal.  
  5. Lagrange stability for asymmetric Duffing equations.
    Yuan, Xiaoping
    Nonlinear Anal. 43 (2001), no. 2, Ser. A: Theory Methods, 137--151, MathSciNet.
  6. The Bifurcation Problems of a Class of Duffing Equation
    Jin, Y.-l.
    Journal- Jishou University Natural Science, 2001, vol. 22, no. 2, pp. 53-56, Ingenta.  
  7. The Effect of Incubation Time Distribution on the Extinction Characteristics of a Rabies Epizootic
    A. C. Fowler
    Bulletin of Mathematical Biology, Vol. 62, No. 4, Jul 2000, pp. 633-655, Ideal.  
  8. Lagrange Stability for Duffing-Type Equations
    Xiaoping Yuan
    Journal of Differential Equations, Vol. 160, No. 1, Jan 2000, pp. 94-117, Ideal.  
  9. Unboundedness in a Duffing Equation with Polynomial Potentials
    Yiqian Wang
    Journal of Differential Equations, Vol. 160, No. 2, Jan 2000, pp. 467-479, Ideal.  
  10. Strategies for the Control of Chaos in a Duffing-Holmes Oscillator
    M. K. Sifakis, S. J. Elliott
    Mechanical Systems and Signal Processing, Vol. 14, No. 6, Nov 2000, pp. 987-1002, Ideal.  
  11. Numerical solution for differential equations of Duffing-type non-linearity using the generalized differential quadrature rule.
    Liu, G. R.; Wu, T. Y.
    J. Sound Vibration 237 (2000), no. 5, 805--817, MathSciNet.
  12. A constructive proof of existence and uniqueness of 2pi-period solution to Duffing equation.
    Weiguo, Li; Zuhe, Shen
    Nonlinear Anal. 42 (2000), no. 7, Ser. A: Theory Methods, 1209--1220, MathSciNet.
  13. Periodic solutions of neutral Duffing equations.
    Zhang, Z. Q.; Wang, Z. C.; Yu, J. S.
    Electron. J. Qual. Theory Differ. Equ. 2000, No. 5, 14 pp. (electronic), MathSciNet.
  14. Imperfect Bifurcation of Systems With Slowly Varying Parameters and Application to Duffing's Equation
    Hua, C.-c.; Lu, Q.-s.
    Applied Mathematics and Mechanics, 2000, vol. 21, no. 9, pp. 1024-1033, Ingenta.  
  15. Analysis of Duffing's oscillator equation with time-dependent parameters.
    Srirangarajan, H.R.; Banait, P.J.
    Journal of Sound and Vibration, 2000, vol. 233, no. 3, pp. 435, Ingenta.  
  16. Derivation of stochastic oscillator of the Duffing type from Lorenz equation and identification of the limit process. Recent trends in stochastic models arising in natural phenomena and the theory of measure-valued stochastic processes (Japanese) (Kyoto, 1999).
    Narita, Kiyomasa
    Surikaisekikenkyusho Kokyuroku No. 1157 (2000), 74--89, MathSciNet.
  17. Multiplicity of Periodic Solutions of Semilinear Duffing's Equation at Resonance
    Zaihong Wang
    Journal of Mathematical Analysis and Applications, Vol. 237, No. 1, Sep 1999, pp. 166-187, Ideal.  
  18. Explicit and exact solutions for the generalized reaction Duffing equation.
    Yan, Zhenya; Zhang, Hongqing
    Commun. Nonlinear Sci. Numer. Simul. 4 (1999), no. 3, 224--227, MathSciNet.
  19. Bifurcation structures generated by the nonautonomous Duffing equation.
    Mira, C.; Touzani-Qriouet, M.; Kawakami, H.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 9 (1999), no. 7, 1363--1379, MathSciNet.
  20. Periodic solutions of Duffing's equations with Henstock integrable forcing term.
    de Lara-Tuprio, Elvira P.
    Proceedings of the International Mathematics Conference (Manila, 1998). Matimyás Mat. 22 (1999), no. 2, 33--38, MathSciNet.
  21. Chaos and Peak-to-Peak Dynamics in a Plankton-Fish Model
    Sergio Rinaldi, Cosimo Solidoro
    Theoretical Population Biology, Vol. 54, No. 1, Aug 1998, pp. 62-77, Ideal.  
  22. Solvability of the Forced Duffing Equation at Resonance
    Chun-Lei Tang
    Journal of Mathematical Analysis and Applications, Vol. 219, No. 1, Mar 1998, pp. 110-124, Ideal.  
  23. Boundedness of Solutions for Semilinear Duffing Equations
    Bin Liu
    Journal of Differential Equations, Vol. 145, No. 1, May 1998, pp. 119-144, Ideal.  
  24. Invariant Tori of Duffing-Type Equations
    Xiaoping Yuan
    Journal of Differential Equations, Vol. 142, No. 2, Jan 1998, pp. 231-262, Ideal.  
  25. Dynamics of a coupled system of Duffing's equations.
    Gong, L.; Wong, Y. S.; Lee, B. H. K.
    Dynam. Contin. Discrete Impuls. Systems 4 (1998), no. 1, 99--119, MathSciNet.
  26. Control of the Chaotic Duffing Equation with Uncertainty in All Parameters.
    Loria, A.; Panteley, E.; Nijmiejer, H.
    IEEE transactions on circuits & systems. Part 1, Fundamental theory and applications, 1998, vol. 45, no. 12, pp. 1252, Ingenta.  
  27. Limit Circles Bifurcated from a Soft Spring Duffing Equation under Perturbation.
    Fude, Cheng
    Applied mathematics and mechanics, 1998, vol. 19, no. 2, pp. 129, Ingenta.  
  28. On Spurious Fixed Points of Runge-Kutta Methods
    F. Vadillo
    Journal of Computational Physics, Vol. 132, No. 1, Mar 1997, pp. 78-90, Ideal.  
  29. One Case of Chaotic Behavior of the Trajectories of Duffing's Equation.
    Martynyuk, A. A.; Nikitina, N. V.
    International applied mechanics, 1997, vol. 33, no. 5, pp. 418, Ingenta.  
  30. On Bifurcations of Periodic Orbits in the van der Pol-Duffing Equation.
    Belyavoka, G.V.; Belyakov, L.A.
    International journal of bifurcation and chaos in applied sciences and engineering, 1997, vol. 7, no. 2, pp. 459, Ingenta.  
  31. Generalized upper and lower solution method for the forced Duffing equation.
    Wang, Chengwen
    Proceedings of the american mathematical society, 1997, vol. 125, no. 2, pp. 397, Ingenta.  
  32. Spatial Chaotic Structure of Attractors of Reaction-Diffusion Systems  
    V. Afraimovich, A. Babin, S.-N. Chow  
    Transactions of the American Mathematical Society, Vol. 348, No. 12. (Dec., 1996), pp. 5031-5063, Jstor.  
  33. Analytical Solution of the Forced Duffing's Oscillator
    M. I. Qaisi
    Journal of Sound and Vibration, Vol. 194, No. 4, Jul 1996, pp. 513-520
  34. Duffing equation with two periodic forcings: The phase effect.
    Yang, Junzhong; Qu, Zhilin; Hu, Gang
    Physical review. E. Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996, vol. 53, no. 5A, pp. 4402, Ingenta.  
  35. Convergence of psi-series solutions of the Duffing equation and the Lorenz system.
    Melkonian, S.; Zypchen, A.
    Nonlinearity 8 (1995), no. 6, 1143--1157, MathSciNet.
  36. Nonlinear Forecasting of Non-Uniform Chaotic Attractors in an Enzyme Reaction  
    L. F. Olsen, K. R. Valeur, T. Geest, C. W. Tidd, W. M. Schaffer  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 348, No. 1688, Chaos and Forecasting. (Sep. 15, 1994), pp. 421-430, Jstor.
  37. Homoclinic Motions and Chaos in the Quasiperiodically Forced Van Der Pol-Duffing Oscillator with Single Well Potential  
    Kazuyuki Yagasaki
    Proceedings: Mathematical and Physical Sciences, Vol. 445, No. 1925. (Jun. 8, 1994), pp. 597-617, Jstor.  
  38. Homoclinic Motions and Chaos in the Quasiperiodically Forced Van Der Pol-Duffing Oscillator with Single Well Potential  
    Kazuyuki Yagasaki  
    Proceedings: Mathematical and Physical Sciences, Vol. 445, No. 1925. (Jun. 8, 1994), pp. 597-617, Jstor.  
  39. Periodically Forced Duffing's Equation
    B. Mehri, M. Ghorashi
    Journal of Sound and Vibration, Vol. 169, No. 3, Jan 1994, pp. 289-295, Ideal.  
  40. Existence and Uniqueness of Periodic Solutions for Duffing Equations across Many Points of Resonance
    H.Z. Wang, Y. Li
    Journal of Differential Equations, Vol. 108, No. 1, Feb 1994, pp. 152-169, Ideal.  
  41. Influence of the excitation shape in the classical Duffing equation.
    Lenci, S.; Tarantino, A.M.
    European journal of mechanics. A/solids, 1994, vol. 13, no. 4, pp. 569, Ingenta.  
  42. The van Kampen Expansion for the Fokker-Planck Equation of a Duffing Oscillator Excited by Colored Noise.
    Weinstein, Edward M.; Benaroya, H.
    Journal of statistical physics, 1994, vol. 77, no. 3/4, pp. 681, Ingenta.  
  43. Chaos in Ecology: Is Mother Nature a Strange Attractor?  
    Alan Hastings, Carole L. Hom, Stephen Ellner, Peter Turchin, H. Charles J. Godfray  
    Annual Review of Ecology and Systematics, Vol. 24. (1993), pp. 1-33, Jstor.  
  44. Existence and Multiplicity Results for Periodic Solutions of Semilinear Duffing Equations
    T.R. Ding, R. Iannacci, F. Zanolin
    Journal of Differential Equations, Vol. 105, No. 2, Oct 1993, pp. 364-409, Ideal.  
  45. Chaos in the Duffing Equation
    F. Battelli, K.J. Palmer
    Journal of Differential Equations, Vol. 101, No. 2, Feb 1993, pp. 276-301, Ideal.  
  46. Solvability of a forced autonomous Duffing's equation with periodic boundary conditions in the presence of damping.
    Gupta, Chaitan P.
    Applications of mathematics, 1993, vol. 38, no. 3, pp. 195, Ingenta.  
  47. An Alternative Analysis of Duffing's Equation (in Classroom Notes)  
    Brian J. McCartin  
    SIAM Review, Vol. 34, No. 3. (Sep., 1992), pp. 482-491, Jstor.  
  48. The First Interval of Stability of a Periodic Equation of Duffing Type  
    Rafael Ortega  
    Proceedings of the American Mathematical Society, Vol. 115, No. 4. (Aug., 1992), pp. 1061-1067, Jstor.  
  49. Experimental mimicry of Duffing's equation.
    Gottwald, J. A.; Virgin, L. N.; Dowell, E. H.
    J. Sound Vibration 158 (1992), no. 3, 447--467, MathSciNet.
  50. Numerical Analysis of Bifurcations in Duffing's Equation with Hysteretic Functions.
    Matsuo, Tetsuji; Kishima, Akira
    Electronics and communications in Japan. Part 3, Fundamental electronic science, 1992, vol. 75, no. 9, pp. 61, Ingenta.  
  51. Dissipative hydrodynamic oscillators. VII. The two-component Lorenz model as a Duffing oscillator, and integrability.
    Sanjuán, M. A. F.; Valero, J. L.; Velarde, M. G.
    Nuovo Cimento D (1) 13 (1991), no. 7, 913--918, MathSciNet.
  52. Dynamical symmetry breaking and chaos in Duffing's equation.
    Olson, Collin L.; Olsson, M.G.
    American journal of physics, 1991, vol. 59, no. 10, pp. 907, Ingenta.  
  53. On the number of solutions of a Duffing equation.
    Fiebig-Wittmaack, M.
    Zeitschrift fur angewandte Mathematik und Physik, 1991, vol. 42, no. 3, pp. 445, Ingenta.  
  54. On the Existence of Stable Periodic Solutions of Differential Equations of Duffing Type  
    A. C. Lazer, P. J. McKenna  
    Proceedings of the American Mathematical Society, Vol. 110, No. 1. (Sep., 1990), pp. 125-133, Jstor.  
  55. Basin Explosions and Escape Phenomena in the Twin-Well Duffing Oscillator: Compound Global Bifurcations Organizing Behaviour  
    Y. Ueda, S. Yoshida, H. B. Stewart, J. M. T. Thompson  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 332, No. 1624. (Jul. 16, 1990), pp. 169-186, Jstor.  
  56. CHAOS and Limit Cycle in Duffing's Equation.
    Ku, Y.H.; Sun, Xiaoguang
    Journal of the Franklin Institute, 1990, vol. 327, no. 2, pp. 165, Ingenta.  
  57. Resonance and Symmetry Breaking for a Duffing Oscillator  
    John Miles, Peter J. Bryant  
    SIAM Journal on Applied Mathematics, Vol. 49, No. 3. (Jun., 1989), pp. 968-981, Jstor.  
  58. 2pi Periodic Solutions of Duffing's Equation with Negative Stiffness  
    J. G. Byatt-Smith  
    SIAM Journal on Applied Mathematics, Vol. 47, No. 1. (Feb., 1987), pp. 60-91, Jstor.  
  59. Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics  
    Celso Grebogi, Edward Ott, James A. Yorke  
    Science, New Series, Vol. 238, No. 4827. (Oct. 30, 1987), pp. 632-638, Jstor.  
  60. On the periodic BVP for the forced Duffing equation.
    Invernizzi, Sergio
    Rend. Istit. Mat. Univ. Trieste 19 (1987), no. 1, 64--75, MathSciNet.
  61. Strange Attractors of Uniform Flows  
    Ittai Kan  
    Transactions of the American Mathematical Society, Vol. 293, No. 1. (Jan., 1986), pp. 135-159, Jstor.  
  62. A Stochastic Model for Nonlinear Oscillators of Duffing Type  
    Renato Spigler  
    SIAM Journal on Applied Mathematics, Vol. 45, No. 6. (Dec., 1985), pp. 990-1005, Jstor.  
  63. Mechanism for chaos in the Duffing equation.
    Elgin, J. N.; Forster, D.; Sarkar, Sarben
    Phys. Lett. A 94 (1983), no. 5, 195--197, MathSciNet.
  64. An Infinite Class of Periodic Solutions of Periodically Perturbed Duffing Equations at Resonance  
    Tung-Ren Ding  
    Proceedings of the American Mathematical Society, Vol. 86, No. 1. (Sep., 1982), pp. 47-54, Jstor.  
  65. Sur la Structure de L'Equation de Duffing Sans Dissipation  
    Bruno V. Schmitt  
    SIAM Journal on Applied Mathematics, Vol. 42, No. 4. (Aug., 1982), pp. 868-894, Jstor.  
  66. Best difference equation approximation to Duffing's equation.
    Potts, Renfrey B.
    J. Austral. Math. Soc. Ser. B 23 (1981/82), no. 4, 349--356, MathSciNet.
  67. Ordinary Differential Equations with Strange Attractors  
    C. J. Marzec, E. A. Spiegel  
    SIAM Journal on Applied Mathematics, Vol. 38, No. 3. (Jun., 1980), pp. 403-421, Jstor.  
  68. Transition Through Resonance of a Duffing Oscillator  
    I. R. Collinge, J. R. Ockendon  
    SIAM Journal on Applied Mathematics, Vol. 37, No. 2. (Oct., 1979), pp. 350-357, Jstor.  
  69. Duffing's equation in brain modelling.
    Zeeman, E. C.
    Papers presented at the Symposium on Excitement in Mathematics (Cambridge, 1975). Bull. Inst. Math. Appl. 12 (1976), no. 7, 207--214, MathSciNet.
  70. Some numerical aspects of the Duffing differential equation. (Spanish)
    Demarée, Gaston; Escobar C., Diego
    Rev. Colombiana Mat. 7 (1973), 45--51, MathSciNet.
  71. Numerical computation of forced oscillations in coupled Duffing equations.
    Van Dooren, René
    Numer. Math. 20 (1972/73), 300--311, MathSciNet.
  72. High Order Resonance for Duffing's Differential Equation  
    Loren P. Meissner  
    SIAM Journal on Applied Mathematics, Vol. 17, No. 2. (Mar., 1969), pp. 240-250, Jstor.  
  73. A Computer Investigation of a Subharmonic Bifurcation Point in the Duffing Equation  
    C. A. Ludeke, J. E. Cornett  
    SIAM Journal on Applied Mathematics, Vol. 14, No. 6. (Nov., 1966), pp. 1298-1306, Jstor.  
  74. A note on periodic solutions of the Duffing equation.
    Struble, Raimond A.
    J. Math. Anal. Appl. 9 1964 498--501, MathSciNet.
  75. A Discussion of the Duffing Problem  
    Raimond A. Struble  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3. (Sep., 1963), pp. 659-666, Jstor.  
  76. Resonant oscillations of the Duffing equation.
    Struble, Raimond A.
    Contributions to Differential Equations 2 1963 485--489 (1963), MathSciNet.
  77. On Duffing's equation.
    Ojalvo, I. U.; Bleckman, G. L.
    J. Appl. Mech. 28 1961 139--140, MathSciNet.
  78. On periodic solutions of Duffing's equation with damping.
    Loud, W. S.
    J. Math. Phys. 34 (1955), 173--178, MathSciNet.

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003