Bifurcation analysis of chaotic geomagnetic field model

The aim of this work is to conduct analytical bifurcation study for exploring the possible varieties of bifurcations and dynamics exist in a new deterministic chaotic system, which models reversals of the Earth magnetic field. First, the basic dynamical properties of the system are analyzed by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Second, the parameters' regions for supercritical and subcritical Andronov-Hopf bifurcations along with the dynamics associated with the codimension two Horozov-Takens bifurcation are studied. Then, the homoclinic bifurcation of the system is analytically investigated. Results reveal that the presence of coexistent attractors in the phase space of the model is possible where they take the forms of equilibria or periodic orbits. Also, it is observed that the existence of homoclinic bifurcation is a key factor that leads to the more complex behaviors and chaos. Finally, numerical simulations are carried out to validate and confirm the results.