A simple fractional-order chaotic system without equilibrium and its synchronization |
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| Affiliation: | 1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;2. Department of Mathematics and Computer Science, University of Tebessa, 12002, Algeria;3. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece;4. Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland;1. Department of Electronics and Communication Engineering, Amity University, Noida, Uttar Pradesh, India;2. Vaagdevi College of Engineering, Warangal, Telengana, India;3. Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Uttar Pradesh, India;1. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Viet Nam;2. Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran;3. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece;4. Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic;5. Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, PR China;6. Ton Duc Thang University, Ho Chi Minh, Viet Nam;1. Unité de recherche de Matière Condensée d’Electronique et de Traitement de Signal (UR-MACETS), Faculty of Sciences, University of Dschang, P.O. Box 69, Dschang, Cameroon;2. Centre for Nonlinear Dynamics (CNLD), Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India;3. Centre d’Excellence Africain en Technologies de l’Information et de la Communication (CETIC), University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon;4. Department of Physics, Nehru Memorial College, Puthanampatti, P.O. 621007, Tiruchirapalli, India;5. Unité de recherche d’Automatique et d’informatique Appliquée (LAIA), IUT-FV de Bandjoun, University of Dschang, Bandjoun, P.O. Box 134, Cameroon;6. Unité de recherche de Mécanique et de Modélisation des Systèmes Physiques (L2MSP), Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 69, Dschang, Cameroon |
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| Abstract: | There has been an increasing interest in discovering no-equilibrium chaotic systems recently. In this paper, a novel three dimensional fractional-order chaotic system, which has no equilibrium, is introduced. Dynamics of the system has been studied. It is interesting that the system can exhibit coexisting chaotic attractors for the order as low as 2.7. The adjustable feature of a variable is studied by introducing a single controlled constant. Circuit implementation of the system is proposed to show its feasibility. In addition, we have designed the controllers to investigate coexisting synchronization types of such a new fractional-order system. Numerical examples have verified the proposed synchronization schemes. |
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| Keywords: | Chaos Equilibrium Hidden attractor Fractional order Control Synchronization |
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