Complex dynamics in a modified disc dynamo: A nonlinear approach

In this article, the complex dynamics of a modified dynamo is studied in detail. A modified disc dynamo is a self-existing disc dynamo that is supposed to be the cause of the magnetic field of Earth, Sun and stars. The stability analysis and chaoticity of the attractor of the modified disc dynamo is discussed in detail. More precisely, using the Lyapunov coefficient, it is proved that the modified disc dynamo system has a subcritical Hopf bifurcation for a specific set of parameters. To strengthen the analytical results, numerical continuation is used to investigate subcritical criteria by computing a Hopf bifurcation diagram. In the process of numerical continuation, some interesting features of the modified disc dynamo are revealed. Subcritical Hopf bifurcation occurs at two points due to the symmetry of equilibrium points.