Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback |
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| Institution: | 1. Faculty of science, Department of Physics, Laboratory of Mechanics, Materials and Structures, University of Yaounde I, PO. Box: 812, Yaounde, Cameroon;2. The African Center of Excellence in Information and Communication Technologies (CETIC), Yaounde, Cameroon;1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, People’s Republic of China;2. College of Mathematics and Information Science, Shaan’xi Normal University, Xi’an 710062, People’s Republic of China |
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| Abstract: | The chaotic behavior of a double-well Duffing oscillator with both delayed displacement and velocity feedbacks under a harmonic excitation is investigated. By means of the Melnikov technique, necessary condition for onset of chaos resulting from homoclinic bifurcation is derived analytically. The analytical results reveal that for negative feedback the presence of time delay lowers the threshold and enlarges the possible chaotic domain in parameter space; while for positive feedback the presence of time delay enhances the threshold and reduces the possible chaotic domain in parameter space, which are further verified numerically through Poincare maps of the original system. Furthermore, the effect of the control gain parameters on the chaotic motion of the original system is studied in detail. |
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