Analytical estimations of limit cycle amplitude for delay-differential equations

Electronic Journal of Qualitative Theory of Differential Equations

Tamás Insperger¹  Gábor Stépán²  Tamás Molnár² 

[1] Budapest University of Technology and Economics, Hungary;Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary;

关键词: delay-differential equation;    hopf bifurcation;    limit cycle;    center manifold reduction;    normal form theory;   

DOI  :  10.14232/ejqtde.2016.1.77

来源: DOAJ

【 摘 要 】

The amplitude of limit cycles arising from Hopf bifurcation is estimated for nonlinear delay-differential equations by means of analytical formulas. An improved analytical estimation is introduced, which allows more accurate quantitative prediction of periodic solutions than the standard approach that formulates the amplitude as a square-root function of the bifurcation parameter. The improved estimation is based on special global properties of the system: the method can be applied if the limit cycle blows up and disappears at a certain value of the bifurcation parameter. As an illustrative example, the improved analytical formula is applied to the problem of stick balancing.

【 授权许可】

Unknown