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A hyperchaotic system without equilibrium |
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| Authors: | Zenghui Wang Shijian Cang Elisha Oketch Ochola Yanxia Sun |
| Institution: | 1. School of Engineering, University of South Africa, Florida, 1710, South Africa 2. Department of Industry Design, Tianjin University of Science and Technology, Tianjin, 300222, P.R. China 3. School of Computing, University of South Africa, Pretoria, 0003, South Africa 4. F??SATI & Department of Electrical Engineering, Tshwane University of Technology, Pretoria, 0001, South Africa |
| Abstract: | This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincaré maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented. |
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