Sinusoidal synchronization of a Duffing oscillator with a chaotic pendulum

In this Letter, analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator are presented. From the analytical conditions, the invariant domain of such sinusoidal synchronization is determined, and the control parameter map of the synchronicity is achieved. Under specific parameters, numerical illustrations of the partial and full sinusoidal synchronizations of the controlled Duffing oscillator with the pendulum are carried out for a better understanding of such synchronization under specific function constraints. The methodology presented in this Letter is applicable to synchronizations with any specific function constraints. -- Highlights: → Synchronization dynamics of two distinct dynamical systems. → Invariant domain of sinusoidal synchronization. → Partial and full sinusoidal synchronizations. → Analytical conditions for sinusoidal synchronization of the pendulum and Duffing oscillator. → Control parameter map for sinusoidal synchronization of the controlled Duffing oscillator with pendulum.