Investigations on the bifurcation of a noisy Duffing–Van der Pol oscillator |
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| Affiliation: | 1. Laboratory of Mechanics and Materials, Department of Physics, Faculty of Science, University of Yaoundé I, Yaoundé, Box 812, Cameroon;2. Fundamental Physics Laboratory, Physics of Complex System group, Department of Physics, Faculty of Science, University of Douala, Douala Box 24 157, Cameroon;3. Department of Sciences and Technologies and Salerno unit of CNISM, University of Sannio, Via Port’Arsa 11, Benevento I-82100, Italy;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 |
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| Abstract: | This study carried out investigations on the bifurcation characteristics of a Duffing–Van der Pol (DVDP) oscillator subjected to white noise excitations. Dynamical (or D-) bifurcations are characterised by dramatic changes in the dynamical behaviour leading to topological changes in the phase portrait. An additional mode of bifurcation - phenomenological (or P-) bifurcation, is observed in stochastically excited systems when the stationary joint probability density function of the state variables undergo topological changes in the probability space. While D-bifurcation analysis is quantified in terms of the sign changes in the largest Lyapunov exponent, P-bifurcation analysis is usually qualitative and through visual inspection. In this study, a new quantitative measure for P-bifurcations based on the Shannon entropy is proposed. A comparison of the parameter regimes of the noisy DVDP oscillator identified by the three bifurcation methodologies have been presented. |
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| Keywords: | Duffing–Van der Pol oscillator D-bifurcation P-bifurcation Gaussian white noise Shannon entropy |
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