Multistability and bifurcations in a 5D segmented disc dynamo with a curve of equilibria

Abstract

Abstract Multistability, i.e., coexisting attractors, is one of the most exciting phenomena in dynamical systems. This paper presents a new category of coexisting hidden attractor: five-dimensional (5D) systems with a curve of equilibria. Based on the segmented disc dynamo, a new 5D hyperchaotic system is proposed. The paper studies not only coexisting self-excited attractors but also coexisting hidden attractors in the new system with four types of equilibria: a curve of equilibria, a line equilibrium, a stable equilibrium, and no equilibria. Furthermore, the paper proves that the degenerate Hopf and pitchfork bifurcations occur in the system. Numerical simulations demonstrate the emergence of the two bifurcations.

Keywords

• 5D segmented disc dynamo
• Curve of equilibria
• Multistability
• Degenerate Hopf bifurcation
• Pitchfork bifurcation