Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 48, pp. 1-9.

Title: Hopf bifurcations and small amplitude limit cycles in
       Rucklidge systems
        
Authors: Fabio Scalco Dias   (Univ. Federal de Itajuba, MG, Brazil)
         Luis Fernando Mello (Univ. Federal de Itajuba, MG, Brazil)

Abstract:
 In this article we study Hopf bifurcations and small amplitude limit
 cycles in a family of quadratic systems in the three dimensional
 space called Rucklidge systems.
 Bifurcation analysis at the equilibria of Rucklidge system is pushed
 forward toward the calculation of the second Lyapunov coefficient,
 which makes possible the determination of the Lyapunov and higher
 order structural stability.


Submitted February 7, 2012. Published February 12, 2013.
Math Subject Classifications: 34A34, 34D20, 34C07.
Key Words: Rucklidge system; limit cycle; stability; Lyapunov coefficient.