We first examine conditions implying monotonicity of the period function for potential systems with a center at 0 (in the whole period annulus). We also present a short comparative survey of the different criteria. We apply these results to quadratic Loud systems for various values of the parameters D and F. In the case of noncritical periods we propose an algorithm to test the monotonicity of the period function for . Our results may be viewed as a contribution to proving (or disproving) a conjecture of Chicone and Jacobs.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-3-5,
author = {A. Raouf Chouikha},
title = {Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {305-325},
zbl = {1161.34020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-3-5}
}
A. Raouf Chouikha. Monotonicity of the period function for some planar differential systems. Part I: Conservative and quadratic systems. Applicationes Mathematicae, Tome 32 (2005) pp. 305-325. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-3-5/