Bibliography for the van der Pol System

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  1. The Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling
    Wirkus S.; Rand R.
    Nonlinear Dynamics, November 2002, vol. 30, no. 3, pp. 205-221(17), Ingenta.
  2. Oscillation-Sliding In A Modified Van Der Pol-Duffing Electronic Oscillator
    Algaba A.; Fernández-Sánchez F.; Freire E.; Gamero E.; Rodríguez-Luis A.J.
    Journal of Sound and Vibration, January 2002, vol. 249, no. 5, pp. 899-907(9), MathSciNet.  
  3. Global bifurcations of periodic orbits in the forced van der Pol equation.
    Guckenheimer, John; Hoffman, Kathleen; Weckesser, Warren
    Global analysis of dynamical systems, 261--276, Inst. Phys., Bristol, 2001, MathSciNet.  
  4. Chaos control of Bonhoeffer-van der Pol oscillator using neural networks
    Ramesh M.; Narayanan S.
    Chaos, Solitons and Fractals, October 2001, vol. 12, no. 13, pp. 2395-2405(11), Ingenta.
  5. A Tame Degenerate Hopf-Pitchfork Bifurcation in a Modified van der Pol--Duffing Oscillator
    Algaba A.; Freire E.; Gamero E.; Rodríguez-Luis A.J.
    Nonlinear Dynamics, July 2000, vol. 22, no. 3, pp. 249-269(21), Ingenta.
  6. A note on the forced Van der Pol equation
    Matzinger E.
    Comptes Rendus de l'Academie des Sciences Series I Mathematics, 15 August 2000, vol. 331, no. 4, pp. 281-286(6), MathSciNet.  
  7. Exceptional complex solutions of the forced van der Pol equation.
    Fruchard, Augustin; Schäfke, Reinhard
    Funkcial. Ekvac. 42 (1999), no. 2, 201--223, MathSciNet.  
  8. The periodic solution of van der Pol's equation.
    Buonomo, A.
    SIAM J. Appl. Math. 59 (1999), no. 1, 156--171 (electronic), MathSciNet.  
  9. Chaos of the relativistic parametrically forced van der Pol oscillator
    Ashkenazy Y.; Goren C.; Horwitz L.P.
    Physics Letters A, 29 June 1998, vol. 243, no. 4, pp. 195-204(10), MathSciNet.  
  10. Orthogonal trajectories and analytical solutions of the van der Pol equation without forcing
    Dixon J.M.; Tuszynski J.A.; Sept D.
    Physics Letters A, 23 February 1998, vol. 239, no. 1, pp. 65-71(7), MathSciNet.  
  11. Van der Pol's oscillator under delayed feedback.
    Atay, F. M.
    J. Sound Vibration 218 (1998), no. 2, 333--339, MathSciNet.  
  12. On a van der Pol type equation with delay in damping.
    Seifert, George
    Quart. Appl. Math. 56 (1998), no. 3, 473--477, MathSciNet.  
  13. Bifurcation and chaos in the double-well Duffing-van der Pol oscillator: numerical and analytical studies.
    Venkatesan, A.; Lakshmanan, M.
    Phys. Rev. E (3) 56 (1997), no. 6, 6321--6330, MathSciNet.  
  14. Limit cycles of cubic van der Pol equation with one finite critical point.
    Guo, Lin; Chen, Guowei
    Ann. Differential Equations 13 (1997), no. 2, 125--139, MathSciNet.  
  15. The Role of Poincare-Andronov-Hopf Bifurcations in the Application of Variable-Coefficient Harmonic Balance to Periodically Forced Nonlinear Oscillators  
    J. L. Summers, J. Brindley, P. H. Gaskell, M. D. Savage  
    Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 354, No. 1704. (Jan. 15, 1996), pp. 143-168, Jstor.  
  16. The Moving Singularities of the Perturbation Expansion of the Classical Kepler Problem  
    Mohammad Tajdari  
    SIAM Journal on Applied Mathematics, Vol. 56, No. 5. (Oct., 1996), pp. 1363-1378, Jstor.  
  17. Investigation of a generalized van der pol oscillator differential equation
    Addo-Asah W.; Akpati H.C.; Mickens R.E.
    Journal of Sound and Vibration, 1995, vol. 179, no. 4, pp. 733-735(3), Ingenta.
  18. Dynamics of two coupled van der Pol oscillators.
    Pastor-Díaz, Ignacio; López-Fraguas, Antonio
    Phys. Rev. E (3) 52 (1995), no. 2, 1480--1489, MathSciNet.  
  19. 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.  
  20. Inverse limits associated with the forced van der Pol equation.
    Holte, Sarah; Roe, Robert
    J. Dynam. Differential Equations 6 (1994), no. 4, 601--612, MathSciNet.  
  21. On the non-integrability of a family of Duffing-van der Pol oscillators
    Bountis T.C.; Drossos L.B.; Lakshmanan M.; Parthasarathy S.
    Journal of Physics A: Mathematical and General, 1993, vol. 26, no. 23, pp. 6927-6942(16), Ingenta.
  22. Two Timescale Harmonic Balance. I. Application to Autonomous One-Dimensional Nonlinear Oscillators  
    J. L. Summers, M. D. Savage  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 340, No. 1659.  (Sep. 15, 1992), pp. 473-501, Jstor.  
  23. Singular Complex Periodic Solutions of Van Der Pol's Equation  
    C. Hunter, M. Tajdari  
    SIAM Journal on Applied Mathematics, Vol. 50, No. 6. (Dec., 1990), pp. 1764-1779, Jstor.  
  24. Resonances and Power Series Solutions of the Forced Van Der Pol Oscillator  
    Mohammad B. Dadfar, James F. Geer  
    SIAM Journal on Applied Mathematics, Vol. 50, No. 5. (Oct., 1990), pp. 1496-1506, Jstor.  
  25. A Period-Adding Phenomenon  
    Mark Levi  
    SIAM Journal on Applied Mathematics, Vol. 50, No. 4. (Aug., 1990), pp. 943-955, Jstor.  
  26. A Phase-Plane Analysis of Bursting in the Three-Dimensional Bonhoeffer-Van Der Pol Equations  
    Son T. Tu  
    SIAM Journal on Applied Mathematics, Vol. 49, No. 2. (Apr., 1989), pp. 331-343, Jstor.  
  27. Dynamics of Two Strongly Coupled Relaxation Oscillators  
    D. W. Storti, R. H. Rand  
    SIAM Journal on Applied Mathematics, Vol. 46, No. 1. (Feb., 1986), pp. 56-67, Jstor.  
  28. Perturbation Analysis of the Limit Cycle of the Free Van Der Pol Equation  
    Mohammad B. Dadfar, James Geer, Carl M. Andersen  
    SIAM Journal on Applied Mathematics, Vol. 44, No. 5. (Oct., 1984), pp. 881-895, Jstor.  
  29. On the Leading Term of the Outer Asymptotic Expansion of Van Der Pol's Equation  
    A. D. MacGillivray  
    SIAM Journal on Applied Mathematics, Vol. 43, No. 6. (Dec., 1983), pp. 1221-1239, Jstor.  
  30. On the Leading Term of the Inner Asymptotic Expansion of Van Der Pol's Equation  
    A. D. MacGillivray  
    SIAM Journal on Applied Mathematics, Vol. 43, No. 3. (Jun., 1983), pp. 594-612, Jstor.  
  31. Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation  
    C. M. Andersen, James F. Geer  
    SIAM Journal on Applied Mathematics, Vol. 42, No. 3. (Jun., 1982), pp. 678-693, Jstor.  
  32. The Stable Self-Excitations of the Nonlinear Wave Equation of Van Der Pol Type  
    R. W. Lardner, G. Nicklason  
    SIAM Journal on Applied Mathematics, Vol. 41, No. 3. (Dec., 1981), pp. 480-492, Jstor.  
  33. Relaxation Oscillations Governed by a Van Der Pol Equation with Periodic Forcing Term  
    J. Grasman, E. J. M. Veling, G. M. Willems  
    SIAM Journal on Applied Mathematics, Vol. 31, No. 4. (Dec., 1976), pp. 667-676, Jstor.  
  34. Analytical Theory of Nonlinear Oscillations. IV: The Periodic Oscillations of the Equation  
    x - epsilon(1 - x^{2n + 2})x + x^{2n + 1} = epsilon a cos(omega t),  a > 0, omega > 0      
    Chike Obi  
    SIAM Journal on Applied Mathematics, Vol. 31, No. 2. (Sep., 1976), pp. 345-357, Jstor.  
  35. Factors and Roots of The Van Der Pol Polynomials  
    F. T. Howard  
    Proceedings of the American Mathematical Society, Vol. 53, No. 1. (Nov., 1975), pp. 1-8, Jstor.  
  36. Measurement of growth rate, non-linear saturation coefficients, and mode-mode coupling coefficients of a `Van der Pol' plasma instability
    Keen B.E.; Fletcher W.H.W.
    Journal of Physics D: Applied Physics, 1970, vol. 3, no. 12, pp. 1868-1885(18), Ingenta.
  37. Van Der Pol's Expressions for the Gamma Function  
    T. S. Nanjundiah  
    Proceedings of the American Mathematical Society, Vol. 9, No. 2. (Apr., 1958), pp. 305-307, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004