In this paper, the dynamics and synchronization of a fractional-order four dimensional nonlinear system based on a two- stage Colpitts oscillator is investigated, using the Grunwald-Letnikov method. The study of the fractional-order stability of the equilibrium states of the system is carried out. The bifurcation diagram confirms the occurrence of Hopf bifurcation in the proposed system when the fractional-order passes a sequence of critical values, and reveals in addition various bifurcation scenarios including period-doubling and interior crisis transitions to chaos. In order to promote chaos-based fractional-order synchronization of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. Numerical simulations are performed to demonstrate the effectiveness and applicability of the proposed technique.
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