Effect of bounded noise on chaotic motion of duffing oscillator under parametric excitation |
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| Institution: | 1. College of Automation and Electrical Engineering, Nanjing Technology University, Nanjing 211816, China;2. Key Laboratory of Advanced Control and Optimization for Chemical Processes, Shanghai 200237, China;3. Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyonsan 38541, Republic of Korea;4. College of Information Science Engineering, Northeastern University, Shenyang 110819, China;1. School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023 Jiangsu, China;2. Advanced Control Systems Laboratory, School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China;3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073 Hubei, China;1. Inria Rennes, France;2. LSV, CNRS, ENS Paris-Saclay, Université Paris-Saclay, France;3. Université de Mons, Belgium;1. School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China;2. School of Software Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China;3. Department of Computer Science, Pace University, New York, NY 10038, USA;4. Department of Computer Science, State University of New York, New York, NY 12561, USA |
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| Abstract: | A harmonic function with constant amplitude and random frequency and phase is called bounded noise. In this paper, the effect of bounded noise on the chaotic behavior of the Duffing oscillator under parametric excitation is studied in detail. The random Melnikov process is derived and a mean-square criterion is used to detect the chaotic dynamics in the system. It is found that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the noise in frequency increases. The threshold of bounded noise amplitude for the onset of chaos is also determined by the numerical calculation of the largest Lyapunov exponents. The effect of bounded noise on the Poincaré map and power spectra is also investigated. The numerical results qualitatively confirm the conclusion drawn by using the random Melnikov process with mean-square criterion for larger noise intensity. |
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