Research and implementation of three-dimensional four-wing chaotic system based on virtual instrument

The software LabVIEW (Laboratory Virtual Instrument Engineering Workbench) is a programming language developed by the American company NI (National Instruments Company). Because LabVIEW uses a graphical programming language based on flowcharts, it is also called G language (Graphics Language). Programs written in G language are called virtual instruments VI (Virtual Instruments). Their interface and functions are very similar to those of real instruments. Applications developed in the LabVIEW environment are all given the suffix VI to indicate virtual instruments. VI consists of a program front panel (Front Panel), a data flow diagram program (Diagram Program) and an icon/terminal (Icon/Terminal).

With the development of modern testing and instrumentation technology, the concept of virtual instrument has developed into an innovative instrument design idea and has become the main method and means for designing complex test instruments and test systems. This paper studies a three-dimensional four-wing chaotic system and designs a virtual instrument chaotic signal generator using LabVIEW. Because this instrument is easy to implement, has high reliability and good real-time performance, compared with traditional autonomous chaotic systems, the chaotic signal output by this instrument is more suitable as an information carrier of a chaotic secure communication system, thereby improving the security of the communication system.

1 Overview of the three-dimensional four-wing chaotic system

Chaos is a form of motion unique to nonlinear dynamic systems, and it is widely present in nature. Generally speaking, chaotic phenomena belong to deterministic systems and are difficult to predict. They are implicit in complex systems but cannot be decomposed, and they present a variety of chaotic and disordered but regular images.

Generating various types of chaotic and hyperchaotic signals suitable for secure communication in nonlinear circuits has been a hot topic in the physics and information science community in recent years. Many related research results have been achieved at home and abroad, such as third-order chaotic circuits, fourth-order variant chaotic circuits, fourth-order MCK hyperchaotic circuits, Lorentz circuits, Cai circuits, hyperchaotic circuits, etc. This paper will use virtual instrument technology to generate three-dimensional four-wing chaotic attractors to generate chaotic signals, and use hardware experimental results to prove that it is correct.

This paper discusses a nonlinear three-dimensional four-wing chaotic system with cubic terms, whose dynamic equation is:

When a=50, b=13, c=13, e=6, and the initial value (1, 1, 1) is selected, the system produces chaotic phenomena.

The actual hardware circuit is composed of operational amplifiers, analog multipliers, etc., and its saturation characteristics must be considered. Therefore, the variable ratio compression transformation of equation (1) is first performed.

In the formula, k is the proportional compression factor of the variable, here k=1/3.

Multiply both sides of equation (1) by k, substitute equation (2), and replace u, v, w with x, y, z to obtain:

[page]

The actual hardware circuit is shown in Figure 1. The circuit consists of four parts: inverting adder module, integrator module, inverter module and cubic term generator module. The operational amplifier model is LF356, the power supply voltage is ±15 V, the linear dynamic range is ±13.5 V, and the multiplier uses AD633. In the experiment, it should be noted that the gain of AD633 is 0.1. In the figure, R1, R2, R5, R6, R13, R14 = 10 kΩ; R4, R9, R16 = 1 kΩ; R3, R8, R15 = 10 kΩ; R16, R11, R18 = 38.46 kΩ; R17 = 83.33 kΩ; R7, R12, R19 = 555 Ω, the multiplier uses AD633, and the operational amplifier is LF356. Here, the three-dimensional four-wing chaotic signal generator is designed by the graphical design language LabVIEW 8.2.

2 Design of the signal generator for the three-dimensional four-wing chaotic system

2.1 Design Principles

The three-dimensional four-wing chaotic system signal generator is designed using the graphical design language LabVIEW 8.2 developed by the American National Instruments Company. With the help of LabVIEW's powerful numerical calculation function, the third-order differential equation (1) is solved, and then the chaotic signal is observed and output through a virtual instrument.

2.2 Specific programming of chaotic system based on LabVIEW

Create a new LabVIEW window, design the front panel in the front panel, and design the flowchart in the back panel.

2.2.1 Front panel design

1) 6 graphic controls, 3 of which display the chaotic time series diagrams of state variables x, y and z, and the other 3 display the phase plane diagrams of state variables x, y and z. Operate Controls>>Graph>>Waveform Graph 3 times, call in 3 graphic controls Graph, and label them as "x time series diagram", "y time series diagram" and "z time series diagram" respectively: Operate Controls>>Graph>>XY Graph 3 times, call in 3 graphic controls, and label them as "xy phase diagram", "xz phase diagram" and "yz phase diagram" respectively.

2) 6 digital controls: They are used to input the initial values ​​x0, y0, and z0 of equation (1). Operate Controls>>Numeric>>Dial 3 times to get 3 input digital controls, labeled "x0", "y0", and "z0"; they are used to input dt and drawing parameters. Operate Controls>>Numefic>>Numeric Control 3 times to get 3 input digital controls, labeled "dr\'', "total number of points to be drawn", and "number of points to be drawn once". [page]

3) A Boolean switch is used to control the program running. Operate Controls>>Boolean>>Stop Button. Set the switch button to "Stop".

Figure 2 is the front panel of the three-dimensional four-wing chaotic signal generator based on the virtual instrument.

2.2.2 Flowchart design

In the flowchart window, execute Funtion>>Structures>>While LooD to create a loop. Right-click on the left and right borders of While Loop, and operate Add Shift Register 6 times each; outside the While Loop border, execute Function>>Array>>Array constant, and set the value to 0; in this While loop, execute Function>>Structures>>Formula Node, and write the differential equation in the formula box; right-click on the left border of Formula Node, and operate Add Input 4 times. Enter "x", "y", "z", and "dt" respectively; right-click on the right border of Formula Node, and operate Add Output 3 times. Enter "dx", "dy", and "dz" respectively; execute Function>>Array>>Build Array three times; execute Function>>Array>>Replace Arrav Subset three times; execute Function>>Array>>Array To Clust-er three times; execute Function>>Numeric>>Conversion>>To Long Integer twice, and enter "Number of Points" and "Points per Draw" respectively; execute Function>>Numeric>>Quotient＆Remainder; execute Function>>Time＆Dialog>>Wait(ms) and enter 0; execute Function>>Boolean>>True constant.

3 Conclusion

This paper uses the LabVIEW virtual instrument technology of the American NI company combined with chaos theory to design and manufacture a three-dimensional four-wing chaotic signal generator based on virtual instruments. The friendly visual graphical interface of LabVIEW allows users to feel the same as operating real instruments when operating. This instrument can be used to easily demonstrate various chaotic states of the chaotic signal generator, and the chaotic signal output can be collected by the data acquisition card. Because this instrument is easy to implement, has high reliability and good real-time performance, compared with traditional autonomous chaotic systems, the chaotic signal output by this instrument is more suitable as an information carrier for encrypted chaotic communication systems, improving the security of communication systems, and also providing a new way to study nonlinear systems.