Abstract
In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.
Highlights
A memristor is a nonlinear two-terminal circuit element reflecting the relationship between charge and magnetic flux, which was first predicted by Chua in 1971 [1]
The randomness of the binary sequences extracted from the above chaotic system were tested by means of the National Institute of Standards and Technology (NIST) test suite [38]
A simple Wien-bridge chaotic circuit based on the absolute memristor was designed
Summary
A memristor is a nonlinear two-terminal circuit element reflecting the relationship between charge and magnetic flux, which was first predicted by Chua in 1971 [1]. A locally active memristor was proposed by Chua, which can generate complex behaviors in nonlinear dynamical systems [4]. Much attention has been paid to construct memristor-based chaotic circuits and analyze their dynamical behaviors. Reference [19] presented and analyzed a new chaotic circuit, which was composed of a meminductor emulator and an active memristor emulator. Reference [20] constructed a memristor-based hyperchaotic Wien-bridge oscillator and analyzed its dynamical behaviors. In Reference [31], the constant Lyapunov exponent spectrum was found in a Wien-bridge chaotic oscillator based on a meminductor. Because of the absence of an inductor, this Wien-bridge circuit is integrated This chaotic system possesses dynamical behaviors, including multistability and sustained chaos state.
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