Hopf bifurcation at the nonzero foci in 1∶4 resonance

• DOI: 10.1007/bf02108858
• Publication Date: 2005-09-13T09:10:16Z
• Authors: Wang Duo
• Keywords: Complex plane; Bar (unit)

The differential equation $$\dot z = e^{i\theta } z + A\left| z \right|^2 z + \bar z^3 ,z \in \mathbb{C}, Re A< 0,Im A< 0$$ in considered, whereθ is a real parameter. We prove that Hopf bifurcation occurs at the nonzero foci and is always subcritical for anyA in a subregion in the complex plane.