^{1,2}

^{1}

^{1}

^{2}

Over the last three decades, theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science. In 2008, the successful development of memristor brings new activity for this research. Memristor is a new nanometre-scale passive circuit element, which possesses memory and nonlinear characteristics. This makes it have a unique charm to attract many researchers’ interests. In this paper, memristor, for the first time, is introduced in a delayed system to design a signal generator to produce chaotic behaviour. By replacing the nonlinear function with memristors in parallel, the memristor oscillator exhibits a chaotic attractor. The simulated results demonstrate that the performance is well predicted by the mathematical analysis and supports the viability of the design.

The memristor, characterized by a relation of the type

Theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science [_{i}O_{2} memristors as nonlinear function is proposed to generate chaotic signals.

In HP’s memristor, a titanium dioxide (T_{i}O_{2}) layer and an oxygen-poor titanium dioxide (T_{i}O_{2-x}) layer are sandwiched between two platinum electrodes, shown as Figure

Structure (a) and symbol (b) of T_{i}O_{2} memristor.

According to the Bernoulli dynamics, we can derive the relation between the charge and magnetic flux as follows [

The

In this section, we design a delayed chaotic system with memristors, which is described by the following first-order delay differential equation:

where

From Section

The parallel circuit of three memristors.

The curves of

In the first-order delay differential equation (

A chaotic attractor of the delayed memristive system (

Time dependence of the state variables

The circuitry implementation of the delayed memristive system: a possible electronic circuit realizing the system is given in Figure

The circuitry implementation of memristive delayed system.

The F

The time-delay circuit block (see Figure

Circuit implementation of the time delay block.

Notably, the T-type LCL unit will bring a little attenuation of the circuit gain. This hurdle can be easily eliminated by operational amplifiers A3 and A4. The circuit parameters are set as follows:

Set

This paper gives a new perspective to understand the performance and application of memristor. The proposed piecewise models are composed by three memristors. We can that find memristor can remember not only the charge (current) but also magnetic flux (voltage). As the nonlinear element, the memristor can also act as an essential nonlinear part in chaotic system. The SPICE models designed in this paper can complete a good simulation work of chaotic circuits, which are expected to produce more rich chaotic attractors.

The work was supported by the National Natural Science Foundation of China under Grants 60972155 and 61101233, the Natural Science Foundation of Chongqing under Grants CSTC2009BB2305, the Fundamental Research Funds for the Central Universities under Grant XDJK2012A007 and XDJK2010C023, the University Excellent Talents supporting Foundations in of Chongqing under Grant 2011-65, the University Key teacher supporting Foundations of Chongqing under Grant 2011-65, the National Science Foundation for Post-doctoral Scientists of China under Grant CPSF20100470116, the Doctoral Foundation of the Southwest University under Grant SWUB2008074, and Spring Sunshine Plan Research Project of Ministry of Education of China under Grant z2011148.