Garira, Winston;
(2002)
Dynamics and synchronisation of two coupled parametric pendula.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
One of the most important discoveries in the study of nonlinear dynamical systems in the last decade is that chaotic systems can be controlled and synchronised. Chaos synchronisation can be viewed as a particular problem of chaos control in the sense that by introducing a coupling term between two independent chaotic systems, we can provide a controlling mechanism in one or both systems (unidirectional or multi-directional coupling) that will eventually cause their trajectories to converge onto each other and then remain synchronised. But in most dynamical systems, chaotic attractors coexist with periodic attractors for a given set of parameters. This guarantees the coexistence of competing synchronous behaviours (chaotic and periodic synchronisation). Therefore in order to fully understand the synchronisation regimes that can occur to a given coupled dynamical system, we need to consider both the chaotic synchronisation component of the dynamics as well as periodic synchronisation and the transition between them. In this thesis we study both periodic and chaotic synchronisation of coupled dynamical systems. We introduce the subject of synchronisation of coupled dynamical systems in chapter 1. In chapters 2, 3 and 4 we study the oscillating, rotating and chaotic solutions of the single parametrically excited pendulum. The study of both periodic and chaotic synchronisation of two coupled parametrically excited pendula (sometimes called pendulums) is considered in chapters 5 and 6 respectively. Then we summarise our main findings in chapter 7 together with some proposals for future research directions.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Dynamics and synchronisation of two coupled parametric pendula |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Thesis digitised by ProQuest. |
| Keywords: | Pure sciences; Chaos synchronisation; Nonlinear dynamical systems |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10102041 |
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