Infinitely many coexisting attractors of a dual memristive Shinriki oscillator and its FPGA digital implementation |
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| Affiliation: | 1. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210023, China;2. School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China;1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA;2. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, PR China;1. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210023, China;2. School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing, 210044, China;1. Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6, Canada;2. Centro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de Leon 1144, Col Paseos de la Montaña, Lagos de Moreno, Jalisco 47463, Mexico;3. Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, 72570 Mexico;4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;5. Laboratory of Nonlinear Systems, Circuits & Complexity, Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece;6. Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi''an 710123, P.R. China;7. Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China;8. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China |
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| Abstract: | In this paper, a novel chaotic oscillator is proposed, which is derived from the classical Shinriki oscillator by substituting the series-parallel diode loop with a flux-controlled memristor and connecting an active charge-controlled memristor in series with an inductor. The mathematical model of the circuit is established, and the stability distribution maps of three non-zero eigenvalues in the equilibrium plane are obtained. The basic dynamical behaviors depending on the variation of the circuit parameters and memristor initial conditions are investigated by standard nonlinear analysis tools, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Particularly, some striking phenomena, including the routes to double-scroll chaotic attractors, coexisting periodic-chaotic bubbles and asymmetric coexisting behaviors are observed. Furthermore, extreme multistability of the new oscillator is revealed by attraction basins under the initial condition of different dynamic elements. Finally, the Shinriki oscillator with two memristors is realized through Field-Programmable Gate Array (i.e., FPGA) to verify the effectiveness of the numerical simulations. |
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