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Title: Design and implementation of grid multi-scroll fractional-order chaotic attractors

Abstract

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

Authors:
;  [1];  [2];  [3];  [4]
  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009 (China)
  2. School of Mathematics, Anhui University, Hefei 230039 (China)
  3. Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto (Portugal)
  4. UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal)
Publication Date:
OSTI Identifier:
22596613
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ATTRACTORS; CHAOS THEORY; COMPUTERIZED SIMULATION; EQUILIBRIUM; LYAPUNOV METHOD; NONLINEAR PROBLEMS; STABILITY

Citation Formats

Chen, Liping, E-mail: lip-chenhut@126.com, Pan, Wei, Wu, Ranchao, Tenreiro Machado, J. A., and Lopes, António M.. Design and implementation of grid multi-scroll fractional-order chaotic attractors. United States: N. p., 2016. Web. doi:10.1063/1.4958717.
Chen, Liping, E-mail: lip-chenhut@126.com, Pan, Wei, Wu, Ranchao, Tenreiro Machado, J. A., & Lopes, António M.. Design and implementation of grid multi-scroll fractional-order chaotic attractors. United States. doi:10.1063/1.4958717.
Chen, Liping, E-mail: lip-chenhut@126.com, Pan, Wei, Wu, Ranchao, Tenreiro Machado, J. A., and Lopes, António M.. 2016. "Design and implementation of grid multi-scroll fractional-order chaotic attractors". United States. doi:10.1063/1.4958717.
@article{osti_22596613,
title = {Design and implementation of grid multi-scroll fractional-order chaotic attractors},
author = {Chen, Liping, E-mail: lip-chenhut@126.com and Pan, Wei and Wu, Ranchao and Tenreiro Machado, J. A. and Lopes, António M.},
abstractNote = {This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.},
doi = {10.1063/1.4958717},
journal = {Chaos (Woodbury, N. Y.)},
number = 8,
volume = 26,
place = {United States},
year = 2016,
month = 8
}
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