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Entropy 2014, 16(12), 6240-6253; doi:10.3390/e16126240

Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems

1
College of Electrical Engineering and Automation, Shandong University of Science and Technology, No. 579, Qianwan'gang Road, Qingdao Economic and Technical Development Zone, Qingdao 266510, China
2
Department of Mathematics, North University of China, No. 3, Xueyuan Road, Jiancaoping District, Taiyuan 030051, China
*
Author to whom correspondence should be addressed.
Received: 1 October 2014 / Revised: 9 November 2014 / Accepted: 21 November 2014 / Published: 28 November 2014
(This article belongs to the Special Issue Recent Advances in Chaos Theory and Complex Networks)
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Abstract

In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems. View Full-Text
Keywords: fractional-order; memristor-based; Lorenz system fractional-order; memristor-based; Lorenz system
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Xi, H.; Li, Y.; Huang, X. Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems. Entropy 2014, 16, 6240-6253.

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