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A.N. Njah, a,
aNonlinear Dynamics Research Group, Department of Physics, University of Agriculture Abeokuta, P.M.B. 2240, Abeokuta, Nigeria
Received 30 December 2008;
revised 8 June 2009;
accepted 15 July 2009.
Handling Editor: M.P. Cartmell.
Available online 18 August 2009.
Abstract
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 Φ6 Van der Pol oscillators (Φ6-VDPOs), two identical Φ6 Duffing oscillators (Φ6-DOs), and two non-identical Φ6 oscillators comprising Φ6-VDPO and Φ6-DO for the triple-well configuration of the Φ6 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.
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