Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems

• Autorzy: A. Raouf Chouikha
• Języki publikacji: EN

Abstrakty

EN

We are interested in conditions under which the two-dimensional autonomous system
ẋ = y, ẏ = -g(x) - f(x)y,
has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.

Kategorie tematyczne

• 37G15: Bifurcations of limit cycles and periodic orbits
• 34C15: Nonlinear oscillations, coupled oscillators
• 34C37: Homoclinic and heteroclinic solutions
• 34C23: Bifurcation
• 34C25: Periodic solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2005
• Tom: 32
• Numer: 4
• Strony: 405-424

Daty

wydano

2005

Twórcy

autor

A. Raouf Chouikha

• LAGA, Université Paris 13, 93430 Villetaneuse, France

Identyfikatory

DOI

10.4064/am32-4-4