Stability and bifurcation analysis of rikitake model

Abstract

In this thesis, stability and bifurcation analysis of Rikitake model was considered. By the aid of divergence, the system is proved to be dissipative. Two Steady state points of the equations were determined. The equations were linearized using Jacobian matrix about each equilibrium points and yield the same characteristic equation. The local stability condition of each critical point was proved by using Routh Huwertiz stability criteria. It is impossible to generalize the global stability property of the two equilibrium point in sense of Lyapunov as one of the condtion is failed to be satisfied. Furthermore, the result of Hopf bifurcation revealed that the system undergoes Hopf bifurcation at the two equilibrium points. Finally, in order to verify the applicability of the result two numerical examples were solved and MATLAB simulation was implemented to support the findings of the study.