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UBC Theses and Dissertations

Construction of chaotic regions for Duffing’s equation with a quadric term Chen, Xiong


Non-linear oscillators can exhibit non-periodic responses under periodic excitation. A point in the parametric space is said to be within a chaotic region if the response under periodic excitation is chaotic. The Lyapunov exponent analysis is developed herein to construct chaotic regions for Duffing's equation. Structural background of Duffing's equation is given. Phase plane and Poincare plots are made to check some questionable chaotic points in the parametric space. In order to help understand chaotic behaviour, bifurcation and stability analyses are presented. Theoretical and heuristic criteria are also discussed for specific cases, and plotted to compare with numerical results. Numerical results are obtained for Duffing's equation with two kinds of quadratic terms, (1) X|X| term, (2) X2 term. Some other cases are also included in order to compare with previous work. In general, good agreement is obtained.

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