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Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control
Authors:Xing-Yuan Wang  Jun-Mei Song
Affiliation:1. Institute for Modern Economics and Management, Zhejiang Yuexiu University, Shaoxing 312000, P. R. China;2. Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6, Canada;3. Department of Banking and Finance, FEMA, University of Malta, MSD 2080, Msida, Malta;5. Department of Management, Faculty of Economics, Management & Accountancy, University of Malta, Msida, Malta;6. Department of Mathematics, Huzhou University, Huzhou 313000, PR China;7. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science Technology, Changsha 410114, PR China;8. Department of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia;1. Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno, 47460, Jalisco, México;2. Facultad de Ingeniería, Universidad Panamericana Josemaría Escrivá de Balaguer 101, Aguascalientes, Aguascalientes, 20290, México;3. Centro de Investigaciones en Óptica, CIO, Loma del Bosque 115, Col. Campestre, León, 37150, GTO, México;4. Applied Mathematics Division, Instituto Potosino de Investigación Científica y Tecnológica, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4ta. Sección, 78216, San Luis Potosí, S. L. P., México;1. Department of Mathematics, University of Larbi Tebessa, Tebessa, 12002 Algeria;2. Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria;3. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan;4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi 100000, Vietnam;6. Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi 100000, Vietnam;7. Universita del Salento, Dipartimento Ingegneria Innovazione, Lecce 73100, Italy
Abstract:Based on the stability theory of fractional order systems, this paper analyses the synchronization conditions of the fractional order chaotic systems with activation feedback method. And the synchronization of commensurate order hyperchaotic Lorenz system of the base order 0.98 is implemented based on this method. Numerical simulations show the effectiveness of this method in a class of fractional order chaotic systems.
Keywords:
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