Chaos resulting from nonlinear relations between different variables |
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| Authors: | Akitaka Dohtani |
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| Institution: | 1. PMB Intelligence LLC, PO Box 2077, West Lafayette, IN 47996, USA;2. LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, People’s Republic of China;3. Affymetrix, Inc., 3380 Central Expressway, Santa Clara, CA 95051, USA;4. Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA;5. Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, USA;1. Department of Economics, LeBow College of Business, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA;2. International Monetary Fund, 700 19th Street, N.W., Washington, DC 20431, USA;1. Department of Economics, Bucknell University, United States;2. Department of Economics, Kansai University, Japan;3. Center for Far Eastern Studies, University of Toyama, Japan;1. Department of Mathematics, Shanghai University, Shanghai 200436, China;2. Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong, China |
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| Abstract: | In this study, we further develop the perturbation method of Marotto 6] and investigate the general mechanisms responsible for nonlinear dynamics, which are typical of multidimensional systems. We focus on the composites of interdependent relations between different variables. First, we prove a general result on chaos, which shows that the cyclic composites of nonlinear interdependent relations are sources of chaotic dynamics in multidimensional systems. By considering several examples, we conclude that the cyclic composites play an important role in detecting chaotic dynamics. |
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