Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations |
| |
| Institution: | 1. School of Economics and Management, Southeast University, Nanjing 211189, Jiangsu, China;2. School of Mathematical Science, Henan Institute of Science and Technology, XinXiang 453003, Henan, China;1. Department of Mechanical and Electrical Engineering, Institute of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon;2. Department of Biomedical Engineering, Amirkabir University of Technology 424 Hafez Ave., Tehran 15875-4413, Iran;3. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;4. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes (LaMSEBP) and TWAS Research Unit, Department of Physics, Faculty of Science, University of Yaoundé I, Po. Box 812, Yaoundé, Cameroon;5. Applied Physics Research Group (APHY), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium;1. Charles M. Bowden Laboratory, U. S. Army Aviation & Missile Res., Dev., & Eng. Center, RDMR-WDS-WO, Redstone Arsenal, AL 35898, USA;2. Torch Technologies, 4035 Chris Dr., Suite C, Huntsville, AL 35802, USA |
| |
| Abstract: | All attempts to generalize the three-dimensional Lorenz model by selecting higher-order Fourier modes can be divided into three categories, namely: vertical, horizontal and vertical–horizontal mode truncations. The previous study showed that the first method allowed only construction of a nine-dimensional system when the selected modes were energy-conserving. The results presented in this paper demonstrate that a five-dimensional model is the lowest-order generalized Lorenz model that can be constructed by the second method and that its route to chaos is the same as that observed in the original Lorenz model. It is shown that the onset of chaos in both systems is determined by a number of modes that describe the vertical temperature difference in a convection roll. In addition, a simple rule that allows selecting modes that conserve energy for each method is derived. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
