Synchronization via active control of identical and non-identical chaotic oscillators with external excitation

Using the active control technique with Lyapunov stability theory and the Routh–Hurwitz criteria, control functions are designed to achieve complete synchronization between two identical Φ 6 Van der Pol oscillators ( Φ 6 -VDPOs), two identical Φ 6 Duffing oscillators ( Φ 6 -DOs), and two non-identical Φ 6 oscillators comprising Φ 6 -VDPO and Φ 6 -DO for the triple-well configuration of the Φ 6 potential. The coefficient matrix of the error dynamics between each pair of synchronized systems is chosen such that the number of active control functions reduces from two to one, thereby, significantly reducing controller complexity in the design. The designed controllers enable the state variables of the response system to synchronize with those of the drive system in both the identical and non-identical cases. The results are validated using numerical simulations.