journal-of-dynamical-systems-and-geometric-theories Journal of Dynamical Systems and Geometric Theories 2169-0057 1726-037X Taru Publications 10.1080/1726037X.2008.10698543 Effect of All Quadratic Terms on Third Order Oscillation Afsharnejad Z. Dept. of Math, Ferdowsi University of Mashhad, Mashhad, Iran Motlagh O. Rabiei Dept. of Math, University of Birjand, Birjand, Iran Tavakoli M. Dept. of Math, Ferdowsi University of Mashhad, Mashhad, Iran 6 1 35 48 03 06 2013

In this paper, we consider non-linear perturbation for the third order linear oscillator. Using the center manifold reduction, we reduced system into second order differential equation. Then we study the Hopf bifurcation of the system and stability of the periodic orbits. At the end we classify the effect of 2-jet of parametric perturbation.

 Center manifold Bifurcation Stability Periodic Solution access open retracted no