Dynamical Properties and Chaos Synchronization in a Fractional-Order Two-Stage Colpitts Oscillator

Abstract

In this paper, the dynamics and synchronization of a fractional-order four dimensional nonlinear system based on a twostage Colpitts oscillator is investigated, using the Grünwald-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.

Keywords

• Colpitts Oscillator
• Fractional-order
• Synchronization
• Hopf Bifurcation
• Nonlinear systems
• Chaos theory. _________________________________________________________________________________