Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-02T00:25:49.858Z Has data issue: false hasContentIssue false

An effective method of counting the number of limit cycles

Published online by Cambridge University Press:  22 January 2016

Kazuo Yamato*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We are interested in determining, after a finite number of procedures, the number and the approximate positions of limit cycles for a given system.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[ 1 ] Cherkas, L. A., Estimation of the number of limit cycles of autonomous systems, Differential Equations 13 (1977), 529547, (transl, from the Russian).Google Scholar
[ 2 ] Comstock, C., On the limit cycles of y″+µF(ý)+у═0, J. Differential Equations 8 (1970), 173179.CrossRefGoogle Scholar
[ 3 ] D’heedene, R. N., For all real has an infinite number of limit cycles, J. Differential Equations 5 (1969), 564571.CrossRefGoogle Scholar
[ 4 ] Graef, J. R., On the generalized Liénard equation with negative damping, J. Differential Equations 12 (1972), 3462.Google Scholar
[ 5 ] Hirsch, M. W. and Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, (1974).Google Scholar
[ 6 ] Hochstadt, H. and Stephan, B. H., On the limit cycles of , Arch. Rational Mech. Anal. 23 (1967), 369379.Google Scholar
[ 7 ] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry I, Interscience Publishers, (1963).Google Scholar
[ 8 ] Salle, J. La and Lefschetz, S., Stability by Liapunov’s Direct Method with Applications, Academic Press, (1961).Google Scholar
[ 9 ] Lefschetz, S., Differential Equations : Geometric Theory, 2nd ed., Interscience Publishers.Google Scholar
[10] Peixoto, M. M., Structural stability on two-dimensional manifolds, Topology 1 (1962), 101120.Google Scholar
[11] Ponzo, P. J. and Wax, N., On periodic solutions of the system -g (x), J. Differential Equations 10 (1971), 262269.Google Scholar
[12] Yamato, K., Qualitative theory of codimension-one foliations, Nagoya Math. J., 49 (1973), 155229.Google Scholar
[13] Bellman, R., Methods of Nonlinear Analysis, Academic Press, Vol. 1 (1970), Vol. 2 (1973).Google Scholar