Bifurcation analysis and integrability in the segmented disc dynamo with mechanical friction

Abstract

Abstract Using center manifold theory, we investigate complex dynamics in a segmented disc dynamo with mechanical friction by making a determination of equilibrium states and analyzing local stability. We find that the system undergoes Hopf bifurcation for a key parameter. Normal form theory produces the formulae for determining a super- or sub-critical Hopf bifurcation; the stability of the bifurcating limit cycle is also determined. In addition, integrability of the system is studied carefully.

Keywords

• Segmented disc dynamo
• Center manifold theory
• Bifurcation
• Chaos
• Normal form theory
• Integrability