Chaotic behaviour in deformable models: the asymmetric doubly periodic oscillators |
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| Institution: | 1. Laboratoire de Mécanique, Faculté des Sciences, Université de Yaoundé I, B.P. 812, Yaoundé, Cameroun;2. Laboratoire de Physique, Faculté des Sciences Mirande, Université de Bourgogne, 9 Aven. A. Savary, B.P. 47870, 21078 Dijon cédex, France;1. Shandong Center of Crop Germplasm Resources, Ji''nan, Shandong, 250100, China;2. Crop Diversification Centre North, Alberta Agriculture and Forestry, Edmonton, AB, T5Y 6H3, Canada;3. Institute of Food Crops, Yunnan Academy of Agricultural Sciences, Kunming, Yunnan, 650205, China;4. Agriculture and Agri-Food Canada (AAFC), Morden, MB, R6M 1Y5, Canada;5. Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB, T6G 2P5, Canada;6. AAFC, Brandon, MB, R7A 5Y3, Canada;1. Guangdong Provincial Key Laboratory of Petrochemical Pollution Processes and Control, School of Environmental Science and Engineering, Guangdong University of Petrochemical Technology, Maoming, Guangdong, 525000, China;2. College of Environmental Science and Engineering, Hunan University and Key Laboratory of Environmental Biology and Pollution Control (Hunan University), Ministry of Education, Changsha, Hunan, 410082, China;3. Datang Environment Industry Group Co., Ltd, Beijing, 100097, China;4. Hunan Provincial Environmental Protection Engineering Center for Organic Pollution Control of Urban Water and Wastewater, Changsha, Hunan, 410001, China;1. Environmental Health Engineering Research Center, Kerman University of Medical Sciences, Kerman, Iran;2. Department of Environmental Health Engineering, Faculty of Public Health, Kerman University of Medical Sciences, Kerman, Iran;3. Department of Public Health, School of Nursing and Midwifery, Iranshahr University of Medical Sciences, Iranshahr, Iran |
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| Abstract: | The motion of a particle in a one-dimensional perturbed asymmetric doubly periodic (ASDP) potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. Theory predicts the regions of chaotic behaviour of orbits in a good agreement with computer calculations. |
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