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Olusola, O. I.; Vincent, U. E.; Njah, A. N.
Abstract
Journal of Sound and Vibration, Volume 329, Issue 4, p. 443-456.
The synchronization dynamics of two linearly coupled pendula is studied in this paper. Based on the Lyapunov stability theory and Linear matrix inequality (LMI); some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling kth, for the on-set of full synchronization is obtained. The numerical value of kth determined from the average energies of the systems is in good agreement with theoretical analysis. Prior to the on-set of synchronization, the boundary crisis of the chaotic attractor is identified. In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition—the basin crisis that occur prior to the on-set of stable synchronization. The essential feature of basin crisis is that the two co-existing attractors are destroyed while new three or more co-existing attractors of the same or different periodicity are created. In addition, the linear perturbation technique and the Routh-Hurwitz criteria are employed to investigate the stability of steady states, and clearly identify the different types of bifurcations likely to be encountered. Finally, two-parameter phase plots, show various regions of chaos, hyperchaos and periodicity.
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