Ivestigation of Some Properties of Lienard Equations

Please enable javascript in your browser.

kanigolzari, Anvar | 2012

595 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42642 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis , we consider the generalized lienard system (dx/dt=1/(a(x)) [h(y)-F(x)])¦(dy/dt=-a(x)g(x) )and under suitable assumptions on a , F , g , h we obtain sufficient and necessary conditions for the intersection of all orbits with the vertical isocline y=F(x) . using these conditions we give some sufficient condition for the oscillation of solutions . then existence and uniqueness of periodic solutions for a kind of lienard equation with a deviating argument are studied . finally we study existence and uniqueness of limit cycles for the generalized lienard system(x ̇=ϕ(y)-F(x))¦(y ̇=-g(x))
Keywords:
Lienard Equation ; Volatility ; Periodic Solution ; Limit Cycles ; Vertical Isocline

No TOC