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Nonlinear Dynamics of The RL-Diode Circuit.

Marsh, Luke. (2006) Nonlinear Dynamics of The RL-Diode Circuit. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

The nonlinear second order differential equation which describes the driven series RL-diode circuit, biased to operate only in the depletion region is given by X + γX + Xμ = α - βsin&tau, where differentiation is with respect to time τ and γ > 0, α > |β| > 0, μ > 1 and X ≥ 0. Without these restrictions and specifically with μ = 2, this differential equation has also been found to exist in a couple of other research contexts, namely in the studies of ship roll and capsize, as well as in a perturbed Korteweg-de Vries equation, where stationary wave solutions are described by a special case of the differential equation. Particular attention is paid firstly to the case μ = 2, which in contrast to Duffing’s equation (μ = 3) has received little attention, and secondly, the case μ = 1.67, which arises from measured values made on a practical diode. The main aim here has been to give a detailed analysis of some properties of the system’s solutions. A rigorous phase plane analysis establishes solution behaviour and a criterion for which solutions grow without bound, before subharmonic solutions of various orders are exhibited. By partitioning the phase plane into regions in which only certain solution behaviour occurs, a variety of invariant sets can be constructed. A numerical scheme which detects unstable periodic orbits is applied to the system, resulting in detection of a set of unstable periodic solutions. This detailed analysis goes some way towards understanding the dynamics of this system.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors : Marsh, Luke.
Date : 2006
Additional Information : Thesis (Ph.D.)--University of Surrey (United Kingdom), 2006.
Depositing User : EPrints Services
Date Deposited : 06 May 2020 13:07
Last Modified : 06 May 2020 13:12
URI: http://epubs.surrey.ac.uk/id/eprint/855940

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