Periodic orbits for an autonomous version of the Duffing–Holmes oscillator

Abstract

In the autonomous Duffing–Holmes oscillator, the existence of periodic orbits was detected numerically. Using the Hopf bifurcation theory, we prove analytically that such periodic orbits exist. We also provide the exact bifurcation value where the Hopf bifurcation takes place.

Keywords

• Hopf bifurcation
• Duffing–Holmes oscillator
• period orbit