Limit cycle uniqueness for a class of planar dynamical systems
Copyright policy )Limit cycle uniqueness for a class of planar dynamical systems
The paper contains the proof of a theorem concerning the uniqueness of a limit cycle for the system \[ \dot{x}=\beta(x)(\varphi(y)-F(x,y)),\quad \dot{y}=-\alpha(y)g(x), \] where \(\alpha(y)\) and \(\beta(x)\) are assumed to be positive. The theorem is applied to such systems in the case \(F(x,y)=F(x)v(y),\) where \(v(y)\) vanishes at some point.
- University of Trento Italy
- University of Florence Italy
limit cycle, Applied Mathematics, limit cycle, uniqueness, Lienard equation, Rayleigh equation, Lotka-Volterra, limit cycle; uniqueness; Lienard equation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, uniqueness, Liénard equation, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Rayleigh equation, Lotka-Volterra system
limit cycle, Applied Mathematics, limit cycle, uniqueness, Lienard equation, Rayleigh equation, Lotka-Volterra, limit cycle; uniqueness; Lienard equation, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, uniqueness, Liénard equation, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Rayleigh equation, Lotka-Volterra system
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).22 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!