Centre bifurcations of periodic orbits for some special three dimensional systems

• Main Authors: Rizgar Salih, Mohammad Hasso
• Format: Article
• Language: English
• Published: University of Szeged 2017-03-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: centre bifurcation; periodic orbits; lü system; liapunov quantities
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5425

In this paper, the bifurcated limit cycles from centre for a special three dimensional quadratic polynomial system and the Lü system are studied. For a given centre, the cyclicity is bounded from below by considering the linear parts of the corresponding Liapunov quantities of the perturbed system. We show that five limit cycles and only one limit cycle can bifurcate from the centres for the three dimensional system and the Lü system respectively.