A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family |
| |
| Authors: | P Yu XX Liao SL Xie YL Fu |
| |
| Institution: | 1. Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7;2. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China;3. School of Electronic and Information Engineering, South China University of Technology, Guangzhou, Guangdong 510640, PR China;2. INRIA Paris-Rocquencourt, Mycenae Team, France;3. LAGA, Université Paris 13, Villetaneuse, France;4. Ecole Normale Supérieure, Département d’Informatique (DATA), 45 rue d’Ulm, 75005 Paris, France;1. Miami University, Oxford, OH 45056, United States;2. University of Iowa, Iowa City, IA 52242, United States;3. Indiana University, Bloomington, IN 47405, United States;1. LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France;2. LOCIE, UMR 5271 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France;3. Université de Nice–Sophia Antipolis, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice cedex 2, France;1. Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515, USA;2. Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;4. Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA 15260, USA |
| |
| Abstract: | In this paper, we give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz systems studied so far in the literature. The system considered in this paper not only contains the classical Lorenz system and the generalized Lorenz family as special cases, but also provides three new Lorenz systems, which do not belong to the generalized Lorenz system, but the general Lorenz system. The results presented in this paper contain all the existing relative results as special cases. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
