Chaos generation in fractional-order switched systems and its digital implementation |
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| Affiliation: | 1. Department of Applied Mathematics, IPICYT, San Luis Potosi, Mexico;2. Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico;3. Mathematics Department, University of Houston, Houston, TX 77204-3008, USA;1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;2. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China;3. National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China;4. State Key Laboratory of Public Big Data, Guizhou 550025, China;1. School of Science, Chongqing University of Posts and Telecommunications, Nanan, 400065 Chongqing, People''s Republic of China;2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070 Gansu, People''s Republic of China;1. Departamento de Matemáticas, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México, D.F., Mexico;2. División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A.C., Camino a la Presa San José 2055 col. Lomas 4a Sección, 78216 San Luis Potosí, SLP, Mexico;3. Departamento de Matemáticas, División de Ciencias Exactas y Naturales, Universidad de Sonora, Boulevard Rosales y Luis Encinas s/n, Col. Centro, 83000 Hermosillo, Sonora, Mexico;1. College of Engineering, Bohai University, Jinzhou, Liaoning 121013, China;2. Chongqing SANY High-Intelligent Robots Co., Ltd., Chongqing 401120, China |
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| Abstract: | A double-scroll chaotic attractor generated by a fractional-order switched system is presented. Based on unstable dissipative systems (UDS) and a switching law, a fractional-order UDS is proposed. Chaos behavior is found with a fractional order as low as 2.568 by satisfying the stability criterion for fractional order chaotic systems. The fractional-order switched system is transformed to an equivalent switched system with augmented states. Then, the equivalent system is straightforward implemented on an ARM system-on-chip board by using Python high level programming language. Numerical simulations are in good agreement with experimental results, which demonstrates the usefulness of proposed method. Additionally, the test 0–1 and a chaos definition for finite state sets are given to demonstrate chaotic behavior. Finally, a random number generator is also proposed as a possible application. |
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| Keywords: | Fractional-order Chaotic attractor Embedded hardware Switched systems ARM architecture |
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