Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Necessary conditions for subharmonic and superharmonic synchronization in weakly nonlinear systems

Authors: Richard E. Kronauer and Samuel A. Musa
Journal: Quart. Appl. Math. 24 (1966), 153-160
MSC: Primary 34.45
DOI: https://doi.org/10.1090/qam/203183
MathSciNet review: 203183
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  • [1] S. Lundquist, Subharmonic Oscillations in a Nonlinear System with Positive Damping, Quart. Appl. Math. 13 (1955) 305-310 MR 0073027
  • [2] M. L. Cartwright, Forced Oscillations in Nonlinear Systems, Contributions to the theory of Nonlinear Oscillations, 1, Princeton University Press, Princeton (1950) 149-241 MR 0035355
  • [3] L. Hansson and K. Goransson, An Experimental Investigation of Subharmonic Oscillations in a Nonlinear System, Trans. Roy. Inst. Technology, Stockholm (1956) MR 0082595
  • [4] H. Poincaré, Les Méthodes nouvelles de la Mécanique Céleste, 1, Gauthier-Villars, Paris (1892) reprint, Dover Publications, Inc., New York (1957)
  • [5] B. Van der Pol, Forced Oscillations in a Circuit with Nonlinear Resistance (Reception with Reactive Triode), Phil. Mag. and J. Sei., 3, (1927) 65-80; reprint, Selected Papers on Mathematical Trends in Control Theory, Dover Publications, Inc., New York, (1964) 124-140
  • [6] N. Krylov and N. Bogoliubov, Introduction to Nonlinear Mechanics, Ann. Math. Studies (1947) No. 11, Princeton Univ. Press, Princeton
  • [7] N. Bogoliubov and Y. Mitropolski, Asymptotic Methods in the Theory of Nonlinear Oscillations (1955) translated by Gordon and Breach, Science Publishers, New York, (1961)
  • [8] J. Cole and J. Kevorkian, Uniformly Valid Asymptotic Approximations for Certain Nonlinear Differential Equations, International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Colorado Springs, Academic Press (1963) 113-120 MR 0147701
  • [9] S. A. Musa, Synchronized Oscillations in Driven Nonlinear Systems, Ph. D. Dissertation, Harvard University, Cambridge, Mass. (1965)
  • [10] R. Gambill and J. Hale, Subharmonic and Ultraharmonic Solutions for Weakly Nonlinear Systems, J. Rati. Mech. Anal. 5 (1956) 353-394. MR 0077741

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DOI: https://doi.org/10.1090/qam/203183
Article copyright: © Copyright 1966 American Mathematical Society

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