Active control of horseshoes chaos in a driven Rayleigh oscillator with fractional order deflection

The problem of suppressing chaos in the Rayleigh oscillator with fractional order deflection is considered. The explanation of Melnikov's techniques shows that the dynamic performance and robustness of the system are highly dependent on the fractional order α. The feedback control system is considered as active control strategy. It is revealed with analytical results that periodic perturbation from the controller enhances the performance of the active control strategy. The proposed control strategy is more efficient for deflection order α element of [1.5,2.5] and under super resonant condition between the driven frequency and perturbation frequency. Numerical simulations demonstrate the effectiveness of Melnikov's analysis. -- Highlights: → Melnikov theorem it applied with an active control strategy. → The Rayleigh oscillator with fractional order deflection is considered. → The horseshoes structure of chaos in analyzed. → The parameter order α influence considerably the control strategy. → The periodic perturbation from the controller enhances the performance of the active control strategy.