We present a new memristor based chaotic circuit, which is generated by replacing the nonlinear resistor in Chua’s circuit with a flux-controlled memristor and a negative conductance. The dynamical behaviors are verified not only by computer simulations but also by Lyapunov exponents, bifurcation analysis, Poincaré mapping, power spectrum analysis, and laboratory experiments.

The memristor was postulated in 1971 by circuit theorist Chua as a missing nonlinear two-terminal electrical component relating electric charge and magnetic flux linkage [

Chaos has great potential application in many engineering fields, such as image encryption and secure communications. As a nonlinear circuit element, the memristor is very suitable for the design of chaotic circuits and the generation of chaotic systems. Some memristor based chaotic circuits were presented by replacing the Chua diodes with memristors characterized by monotone-increasing piecewise-linear function [

In this paper, a memristor based chaotic circuit is presented by replacing the nonlinear resistor in Chua’s circuit with a flux-controlled memristor which is characterized by a smooth cubic nonlinear resistor. The rest of this paper is organized as follows. The new chaotic circuit with memristor and the corresponding mathematical model are presented in Section

The two nonlinear functions

The memristor used in this paper is a flux-controlled memristor, and we assume that the flux-controlled memristor is characterized by a smooth continuous cubic monotone-increasing nonlinearity as follows:

In view of (

The memristor based chaotic circuit is shown in Figure

Chua’s circuit with a flux-controlled memristor.

Applying Kirchhoff’s voltage and current laws and component’s current-voltage relationship to the circuit in Figure

Equation (

Take

Phase portraits of the chaotic system (

Similar to dynamical analysis of general chaotic circuits, by using the conventional dynamical analysis methods, such as bifurcation diagram, Lyapunov exponent spectra, the dynamical behaviors of the chaotic system (

Holding the values of

The Lyapunov exponents in the (

Bifurcation diagram for increasing

It can be seen from Figures

When

When

When

When

When

When

When

Phase portraits of system (

Poincaré mapping is shown in Figure

Poincaré mapping of system (

The power spectrum of system (

Power spectrum of system (

In this section, we present experimental confirmation of the above numerical results through Multisim modeling. The circuit is designed as in Figure

The chaotic circuit.

The two-terminal memristor consists of five Op-Amps TL084, two analog multipliers AD633, thirteen resistors, and three capacitances. The parameter values of the circuit are

Phase portraits of system (

In this paper, we present a memristor chaotic circuit, which is derived from Chua’s oscillator by replacing Chua’s diode with a charge-controlled memristor. This chaotic circuit uses only four basic circuit elements and has only one negative element in addition to the nonlinearity. The resulting chaotic system is demonstrated by computer simulations and verified by Lyapunov exponents, bifurcation, poincaré mapping, and power spectrum analysis.

This research was supported by the National Natural Science Foundation of China (Grant no. 60971022 and no. 61004078).