Relaxation oscillations
Author:
J. LaSalle
Journal:
Quart. Appl. Math. 7 (1949), 1-19
MSC:
Primary 36.0X
DOI:
https://doi.org/10.1090/qam/30075
MathSciNet review:
30075
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Additional Information
E. and H. Cartan, Note sur la génération des oscillations entretenues, Ann. des Post Télégr. Téléph. 12, 1196–1207 (1925).
B. van der Pol, On “relaxation oscillations”, Phil. Mag. 27, 978–992 (1926).
B. van der Pol, Oscillations sinusoidales et de relaxation, l’Onde Electrique 9, 293–312 (1930).
B. van der Pol, The non-linear theory of electrical oscillations, Proc. Instit. Radio Eng. 22, 1051-1086 (1934).
A. Liénard, Etude des oscillations entretenues, Rev. Gén. de l’Elec. 23, 901-912 and 946-954 (1928).
- Norman Levinson and Oliver K. Smith, A general equation for relaxation oscillations, Duke Math. J. 9 (1942), 382–403. MR 6792
- J. Haag, Étude asymptotique des oscillations de relaxation, Ann. Sci. École Norm. Sup. (3) 60 (1943), 35–64, 65–111 (French). MR 0014538
- A. A. Andronow and C. E. Chaikin, Theory of Oscillations, Princeton University Press, Princeton, N. J., 1949. English Language Edition Edited Under the Direction of Solomon Lefschetz. MR 0029027
- D. A. Flanders and J. J. Stoker, The limit case of relaxation oscillations, Studies in Nonlinear Vibration Theory, Institute for Mathematics and Mechanics, New York University, 1946, pp. 50–64. MR 0018780
- Norman Levinson, Perturbations of discontinuous solutions of nonlinear systems of differential equations, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 214–218. MR 22010, DOI https://doi.org/10.1073/pnas.33.7.214
- Solomon Lefschetz, Lectures on Differential Equations, Annals of Mathematics Studies, No. 14, Princeton Univeristy Press, Princeton, N. J.; Oxford University Press, London, 1946. MR 0016788
- V. V. Kazakevitch, On approximate integration of van der Pohl’s equation, C. R. (Doklady) Acad. Sci. URSS (N. S.) 49 (1945), 414–417. MR 0016790
E. and H. Cartan, Note sur la génération des oscillations entretenues, Ann. des Post Télégr. Téléph. 12, 1196–1207 (1925).
B. van der Pol, On “relaxation oscillations”, Phil. Mag. 27, 978–992 (1926).
B. van der Pol, Oscillations sinusoidales et de relaxation, l’Onde Electrique 9, 293–312 (1930).
B. van der Pol, The non-linear theory of electrical oscillations, Proc. Instit. Radio Eng. 22, 1051-1086 (1934).
A. Liénard, Etude des oscillations entretenues, Rev. Gén. de l’Elec. 23, 901-912 and 946-954 (1928).
N. Levinson and O. Smith, A general equation for relaxation oscillations, Duke Math. Jour. 9, 382-403 (1942).
J. Haag, Etude asymptotique des oscillations de relaxation, Ann. Sci. École Norm. Sup. (3) 60, 35-64, 65-111 and 61, pp. 73-117 (1944).
A. Andronow and C. Chaikin, Theory of oscillations, English Language Edition, Princeton Univ., 1948.
D. Flanders and J. Stoker, The limit case of relaxation oscillations. Studies in Non-Linear Vibration Theory, New York Univ., 1946.
N. Levinson, Perturbations of discontinuous solutions of non-linear systems of differential equations, Proc. Nat. Acad. Sci. 33, 214-218 (1947).
S. Lefschetz, Lectures on differential equations, Princeton Univ., 1946.
U. Kazakevich, On approximate integration of van der Pol’s equation, Doklady Akad. Nauk SSSR (N.S.) 49, 414-417 (1945).
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Article copyright:
© Copyright 1949
American Mathematical Society
