Keywords : center manifold and normal form


Limit Cycles of Lorenz System with Hopf Bifurcation

Azad I. Amen; Rizgar H. Salih

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 81-99
DOI: 10.33899/csmj.2008.163951

We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the results presented in this paper.