DOI: 10.36347/sjpms.2023.v10i06.002

Pages: 132-139

In this study, the stability and Hopf bifurcation analysis of periodic solutions of Duffing equations were considered. Also other types of bifurcation like the Saddle-node, Transcritical and Pitchkfork were also studied. The eigen value, Jacobian and Floquet theory were used to analyse both the stability and Hopf bifurcations of the periodic solutions of the equilibrium points. The results showed that equilibrium points have at most three -periodic solutions under a strong damped conditions due to the cubic nonlinearities. The bifurcation points showed; one critical, another subcritical and the third point showed that the homoclinic was present when the damping coefficient is zero. Furthermore, the presence of strange attractors varied with the driving force and damping. The MATCAD software was used to illustrate the numerical behaviour of the solution which extend some results in the literature.