Fractional-order attractors synthesis via parameter switchings |
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| Institution: | 1. Department of Mathematics and Computer Science, Avram Iancu University, Str. Ilie Macelaru nr. 1A, 400380 Cluj-Napoca, Romania;2. Romanian Institute of Science and Technology, Str. Ciresilor nr. 29, 400487 Cluj-Napoca, Romania;3. Institut Computational Mathematics, Technische Universität Braunschweig, Pockelsstr. 14, 38106 Braunschweig, Germany;4. Gesellschaft für Numerische Simulation mbH, Am Gaußberg 2, 38114 Braunschweig, Germany;1. Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno, Czech Republic;2. Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia;3. Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia;4. Centre for Research and Utilization of Renewable Energy, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno, Czech Republic;1. Universidad Internacional de La Rioja, Departamento de ordenación docente, 26002 Logroño, La Rioja, Spain;2. Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA;1. Faculty of Information Engineering, China University of Geosciences, Wuhan, China;2. Services Computing Technology and System Lab/Cluster and Grid Computing Lab/Big Data Technology and System Lab, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China;3. Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan, China;1. Department of Industrial Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran;2. Department of Industrial Engineering, Faculty of Engineering and Technology, University of Qom, Qom, Iran |
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| Abstract: | In this paper we provide numerical evidence, via graphics generated with the help of computer simulations, that switching the control parameter of a dynamical system belonging to a class of fractional-order systems in a deterministic way, one obtains an attractor which belongs to the class of all admissible attractors of the considered system. For this purpose, while a multistep numerical method for fractional-order differential equations approximates the solution to the mathematical model, the control parameter is switched periodically every few integration steps. The switch is made inside of a considered set of admissible parameter values. Moreover, the synthesized attractor matches the attractor obtained with the control parameter replaced with the averaged switched parameter values. The results are verified in this paper on a representative system, the fractional-order Lü system. In this way we were able to extend the applicability of the algorithm presented in earlier papers using a numerical method for fractional differential equations. |
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