Next Article in Journal
On a Local Fractional Wave Equation under Fixed Entropy Arising in Fractal Hydrodynamics
Next Article in Special Issue
A Color Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System
Previous Article in Journal
Ordinal Patterns, Entropy, and EEG
Previous Article in Special Issue
The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map
Open AccessArticle

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

by Huiling Xi 1,2, Yuxia Li 1,* and Xia Huang 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
Department of Mathematics, North University of China, No. 3, Xueyuan Road, Jiancaoping District, Taiyuan 030051, China
Author to whom correspondence should be addressed.
Entropy 2014, 16(12), 6240-6253;
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)
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
Show Figures

Graphical abstract

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Article Access Map by Country/Region

Only visits after 24 November 2015 are recorded.
Search more from Scilit
Back to TopTop