Centre Bifurcations for a Three Dimensional System with Quadratic Terms

  • Rizgar Haji Salih Department of Mathematics, College of Basic Education, University of Raparin, Kurdistan Region-Iraq
  • Mohammed Shami Hasso Department of Mathematics, Faculty of Science and Health, Koya University, Kurdistan Region-Iraq
  • Surma H. Ibrahim Department of Mathematics, Koya University, Faculty of Science and Health, Kurdistan Region-Iraq
Keywords: Hopf and Centre Bifurcation; Periodic Solutions; Inverse Jacobi Multiplier.

Abstract

This article is devoted to study the bifurcated periodic orbits from centre for a differential equation of third order. Sufficient conditions for the existence of a centre are obtained by using inverse Jacobi multiplier. As a result, we found four sets of centre conditions on the centre manifold. For a given centre, it is shown that three periodic orbits can be bifurcated from the origin under two sets of condition and four periodic orbits under the other sets of condition. The cyclicityes are obtained by considering the linear parts of the corresponding Liapunov quantities of the perturbed system.

Author Biography

Rizgar Haji Salih, Department of Mathematics, College of Basic Education, University of Raparin, Kurdistan Region-Iraq

College of Science

References

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Published
2020-04-22
How to Cite
Salih, R., Hasso, M. and Ibrahim, S. (2020) “Centre Bifurcations for a Three Dimensional System with Quadratic Terms”, Zanco Journal of Pure and Applied Sciences, 32(2), pp. 62-71. doi: 10.21271/ZJPAS.32.2.7.
Section
Mathematics ,Physics and Engineering Researches