On Limit Cycles of Planar Dynamical System Via Dulac- Cherkas Function

Azad Ibrahim Amen

Department of Mathematics, College of Basic Education/University of Salahaddin-Hawler-Iraq.

DOI: https://doi.org/10.17656/jzs.10379

Abstract

The main aim of this paper is to construct Bendixson-Dulac and Dulac-Cherkas functions

to study the maximum number of limit cycles for several families of planar dynamical

system. We also apply the results to Lienard and biochemistry reaction systems. 

Key Words: Limit cycles Bendixson function Dulac-Cherkas function planar vector field 

References

[1]Chavarriga J. and Grau M. Some open problems related to 16th Hilbert problem. Series A: Mathematical Sciences, Vol. 9 (2003), 1–26.

[2]Cherkas L. ,Grin A., and Schneider K.R.Dulac-Cherkas functions for generalizedLienard systems. Elec.J. Qual.Theo.Diff.Eqs.35(2011)1-23.

[3]Cherkas L. and GrinA..Bendixson-Dulac criterion and reducation to global uniqueness in the problem of estimating the number of limit cycles.Diff,Eqs. vo.46,no.1(2010)61-69.

[4]Cherkas L. and GrinA..On a Dulac function for the Kuklessystem.Diff,Eqs. vo.46,no.6(2010)818-826.

[5]Gasull A. andGiacominiH..Some applications of the extended Bendixson-Dulactheorem.preprint, arXiv: 1035.3402(2013).

[6]GineJ.Dulac functions of planar vector fields.Qual.Theo.Dyn.Sys.vol.13 (2014)121-128.

[7]LiuX.G.Limit cycles in a class of biochemistry reaction systems. Dyn. Cont.Disc. Imp.Sys.A.Math. Ana.12(2005)675-684.

[8]Odani K., The integration of polynomial Li ́enard systems by elementary functions, Diff. Eqs.Dyn. Sys 5(3-4) (1997) 347–354, Planar nonlinear dynamical systems (Delft, 1995).  

View Full Article