Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-19T09:29:13.536Z Has data issue: false hasContentIssue false
  • English
  • Français

On the non-autonomous van der Pol equation with large parameter

Published online by Cambridge University Press:  24 October 2008

N. G. Lloyd
N. G. Lloyd
Affiliation:
St John's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

We consider the equation

.

where ø = λt + μ; the dot denotes differentiation with respect to a real variable t (frequently for convenience called ‘time’); b, λ, k, μ are parameters independent of x, ẋ t and b, λ, μ independent of k.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 213 - 227
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Cartwright, M. L.Forced oscillations in nonlinear systems. Contributions to the theory of nonlinear oscillations, Vol. 1 (Annals of Mathematics studies No. 20, Princeton, 1950).Google Scholar
(2)Cartwright, M. L. and Littlewood, J. E.On nonlinear differential equations of the second order, I. J. London Math. Soc. 20 (1945), 180–189.CrossRefGoogle Scholar
(3)Hale, J. K.Oscillations in nonlinear systems (McGraw-Hill, 1963).Google Scholar
(4)Littlewood, J. E.On nonlinear differential equations of the second order, III. Acta Math. 97 (1957), 267–308.Google Scholar
(5)Littlewood, J. E.On nonlinear differential equations of the second order, IV. Acta Math. 98 (1957), 1–110.CrossRefGoogle Scholar
(6)Littlewood, J. E.Some problems in real and complex analysis (Heath, 1968).Google Scholar
(7)Wendel, J. G.Singular perturbations of a van der Pol equation. Contributions to the theory of nonlinear oscillations, Vol. 1 (Annals of Mathematics studies No. 20, Princeton, 1950).Google Scholar