Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
The chaotic behaviors of the Arneodo’s system are investigated in this paper. Based on the Arneodo's system characteristic equation, the equilibria of the system and the conditions of Hopf bifurcations are obtained, which shows that Hopf bifurcations occur in this system. Then using the normal form theory, we give the explicit formulas which determine the stability of bifurcating periodic solutions and the direction of the Hopf bifurcation. Finally, some numerical examples are employed to demonstrate the effectiveness of the theoretical analysis.
Y. J. Liu et al., "Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System", Applied Mechanics and Materials, Vols. 130-134, pp. 2550-2557, 2012