scholarly journals Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems

2007 ◽  
Vol 34 (4) ◽  
pp. 1307-1317 ◽  
Author(s):  
J.L. López ◽  
R. López-Ruiz
Keyword(s):  
Limit Cycles ◽  
Nonlinear Regime ◽  
Weakly Nonlinear ◽  
Liénard Systems

scholarly journals BIFURCATION CURVES OF LIMIT CYCLES IN SOME LIÉNARD SYSTEMS

2000 ◽  
Vol 10 (05) ◽  
pp. 971-980 ◽  
Author(s):  
R. LÓPEZ-RUIZ ◽  
J. L. LÓPEZ
Keyword(s):  
Continuous Function ◽  
Limit Cycles ◽  
Nonlinear Regime ◽  
Liénard Systems

Liénard systems of the form [Formula: see text], with f(x) an even continuous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak (ε → 0) and in the strongly (ε → ∞) nonlinear regime in some examples. The number of limit cycles does not increase when ε increases from zero to infinity in all the cases analyzed.

The Linear and Weakly-Nonlinear Stability of a Core Annular Flow in a Corrugated Tube

2000 ◽  
Author(s):  
Hsien-Hung Wei ◽  
David S. Rumschitzki
Keyword(s):  
Thin Film ◽  
Nonlinear Stability ◽  
Annular Flow ◽  
Linear Instability ◽  
Base Flow ◽  
Nonlinear Regime ◽  
Weakly Nonlinear ◽  
Corrugated Tube

Abstract Both linear and weakly nonlinear stability of a core annular flow in a corrugated tube in the limit of thin film and small corrugation are examined. Asymptotic techniques are used to derive the corrugated base flow and corresponding linear and weakly nonlinear stability equations. Interesting features show that the corrugation interaction can excite linear instability, but the nonlinearity still can suppress such instability in the weakly nonlinear regime.

scholarly journals Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Yanqin Xiong ◽  
Maoan Han
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Special Form ◽  
Bifurcation Of Limit Cycles ◽  
Liénard Systems

We consider a class of discontinuous Liénard systems and study the number of limit cycles bifurcated from the origin when parameters vary. We establish a method of studying cyclicity of the system at the origin. As an application, we discuss some discontinuous Liénard systems of special form and study the cyclicity near the origin.

scholarly journals Limit cycles in Liénard systems with saturation

2018 ◽  
Vol 51 (33) ◽  
pp. 127-131
Author(s):  
Thomas Lathuilière ◽  
Giorgio Valmorbida ◽  
Elena Panteley
Keyword(s):  
Limit Cycles ◽  
Liénard Systems
Sign in / Sign up

Export Citation Format

Share Document