Bifurcations of the forced van der Pol oscillator
Open Access
- 1 January 1978
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 35 (4) , 495-509
- https://doi.org/10.1090/qam/492551
Abstract
We discuss the bifurcations of the variational equation of the forced van der Pol oscillator and prove the existence of bifurcations of saddle connection type as postulated by M. L. Cartwright [4] and A. W. Gillies [5].Keywords
This publication has 11 references indexed in Scilit:
- Morse inequalities for diffeomorphisms with shoes and flows with solenoidsPublished by Springer Nature ,1975
- Generic one-parameter families of vector fields on two-dimensional manifoldsPublications mathématiques de l'IHÉS, 1974
- Singularities of vector fieldsPublications mathématiques de l'IHÉS, 1974
- Invariant manifoldsBulletin of the American Mathematical Society, 1970
- Differentiable dynamical systemsBulletin of the American Mathematical Society, 1967
- ON THE TRANSFORMATIONS OF SINGULARITIES AND LIMIT CYCLES OF THE VARIATIONAL EQUATIONS OF VAN DER POLThe Quarterly Journal of Mechanics and Applied Mathematics, 1954
- IV. FORCED OSCILLATIONS IN NONLINEAR SYSTEMSPublished by Walter de Gruyter GmbH ,1950
- A Second Order Differential Equation with Singular SolutionsAnnals of Mathematics, 1949
- Forced oscillations in nearly sinusoidal systemsJournal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering, 1948
- On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y 2 )y˙ + y = b λk cos(λl + α), k LargeJournal of the London Mathematical Society, 1945