Chaos in a new fractional-order system without equilibrium points |
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| Affiliation: | 1. Departamento de Física y Matemáticas, Universidad Iberoamericana, Ciudad de México, México;2. Departamento de Física, Universidad Autónoma de la Ciudad de México, Ciudad de México, México;3. Departamento de Ingenierías, Universidad Iberoamericana, Ciudad de México, México;1. School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, 330013, China;2. Laboratory of Electronics and Signal Processing, Department of Physics, University of Dschang, Dschang, P.O. Box 67, Cameroon;3. Laboratory of Automation and Applied Computer, Department of Electrical Engineering, University of Dschang, Bandjoun, P. O. Box 134, Cameroon;4. School of Mathematics, Hefei University of Technology, Hefei, 230009, China |
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| Abstract: | Chaotic systems without equilibrium points represent an almost unexplored field of research, since they can have neither homoclinic nor heteroclinic orbits and the Shilnikov method cannot be used to demonstrate the presence of chaos. In this paper a new fractional-order chaotic system with no equilibrium points is presented. The proposed system can be considered “elegant” in the sense given by Sprott, since the corresponding system equations contain very few terms and the system parameters have a minimum of digits. When the system order is as low as 2.94, the dynamic behavior is analyzed using the predictor–corrector algorithm and the presence of chaos in the absence of equilibria is validated by applying three different methods. Finally, an example of observer-based synchronization applied to the proposed chaotic fractional-order system is illustrated. |
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| Keywords: | Chaotic dynamics Fractional calculus Equilibrium points Predictor–corrector algorithm Lyapunov exponents |
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