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.
Highlights
The memristor, a nonlinear resistor with a memory effect, was originally postulated by Chua in [1]
In [19], a fourth degree polynomial memristance function is used in the fractional-order memristor-based simplest chaotic circuit
We first propose a new fractional-order memristor-based Lorenz system with the flux-controlled memristor characterized by a piecewise linear function, and its dynamical behaviors are illustrated by using a phase portrait, a bifurcation diagram, the largest lyapunov exponent and a power spectrum diagram
Summary
The memristor, a nonlinear resistor with a memory effect, was originally postulated by Chua in. Research has been done on the charge-controlled memristor characterized by a fourth degree polynomial function [19]. In [19], a fourth degree polynomial memristance function is used in the fractional-order memristor-based simplest chaotic circuit. The above-mentioned research results focus on the fractional-order memristor-based Chua or the simplest circuit. The idea of developing the fraction-order memristor-based Lorenz system with a piecewise linear function arose. We first propose a new fractional-order memristor-based Lorenz system with the flux-controlled memristor characterized by a piecewise linear function, and its dynamical behaviors are illustrated by using a phase portrait, a bifurcation diagram, the largest lyapunov exponent and a power spectrum diagram. Simulation results show that these fractional-order memristor-based systems exhibit some interesting dynamical behaviors within a certain range of parameters.
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