CN108022488B - A four-dimensional coupled power generation hyperchaotic system simulation circuit - Google Patents
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Abstract
一种四维耦合发电超混沌系统模拟电路，包括第一通道的输出端连接第一通道的输入端、第二通道的第一输入端和接第三通道中乘法器A1的输入引脚；第一通道输出端的前一级输出端连接第二通道中的乘法器A2的第一输入引脚；第二通道的输出端连接第二通道的第二输入端、第四通道的输入端；第二通道输出端的前一级输出端连接第一通道的第二输入端、第一通道中乘法器A3的第一输入引脚和第三通道中乘法器A1的第二输入引脚；第三通道输出端的前一级输出端连接第一通道中乘法器A3的第二输入引脚、第二通道的乘法器A2的第二输入引脚和第三通道的输入端；第四通道输出端的前一级输出端连接第一通道的第三输入端；本发明具有电路结构简单，容易实现的优点。
A four-dimensional coupled power generation hyperchaotic system analog circuit, comprising an output end of a first channel connected to an input end of the first channel, a first input end of a second channel and an input pin connected to a multiplier A1 in the third channel; The output end of the previous stage of the channel output end is connected to the first input pin of the multiplier A2 in the second channel; the output end of the second channel is connected to the second input end of the second channel and the input end of the fourth channel; the second channel The output end of the previous stage of the output end is connected to the second input end of the first channel, the first input pin of the multiplier A3 in the first channel and the second input pin of the multiplier A1 in the third channel; The output terminal of the previous stage is connected to the second input pin of the multiplier A3 in the first channel, the second input pin of the multiplier A2 of the second channel and the input terminal of the third channel; the previous stage output of the output terminal of the fourth channel The terminal is connected to the third input terminal of the first channel; the invention has the advantages of simple circuit structure and easy realization.
Description
技术领域technical field
本发明涉及非线性信号发生器装置设计技术领域,特别涉及一种四维耦合发电超混沌系统模拟电路。The invention relates to the technical field of nonlinear signal generator device design, in particular to a four-dimensional coupled power generation hyperchaotic system analog circuit.
背景技术Background technique
混沌系统在电路、通信、信息科学、工程技术以及医学等有着广泛的应用，也被人们普通认同。地磁场长期变化中的极性反转，是地磁理论中最难以说明的问题之一，对此地磁学家提出了许多模型描述其现象，其中耦合发电机模型是最早的且是最为经典的模型。而随着人们对自然界的认识，发现地磁模型复杂度为高维系统，基于此，人们从三维的基础上，提出了维数更高的系统即四维耦合发电超混沌系统，但对于此模型的分析文献较多，其电路实现文献与专利均未报道。Chaos systems have a wide range of applications in circuits, communications, information science, engineering technology, and medicine, and are generally recognized by people. The polarity reversal in the long-term changes of the geomagnetic field is one of the most difficult problems to explain in geomagnetic theory. Geomagnetists have proposed many models to describe its phenomenon, among which the coupled generator model is the earliest and the most classic model. . With people's understanding of nature, it is found that the complexity of the geomagnetic model is a high-dimensional system. Based on this, people have proposed a higher-dimensional system on the basis of three-dimensionality, that is, a four-dimensional coupled power generation hyperchaotic system. There are many analysis literatures, but neither the circuit realization literature nor the patent report.
目前，混沌系统的实现即沌电路的实现，则设计四维耦合发电机超混沌系统电路，对于认识与分析磁极性反转有着重要应用价值。本发明所要解决的现有技术的缺点即高维地磁耦合发电系统不易用电路实现以及电路不可靠性等问题。At present, the realization of the chaotic system is the realization of the chaotic circuit, and the design of the hyperchaotic system circuit of the four-dimensional coupled generator has important application value for understanding and analyzing the magnetic polarity reversal. The disadvantages of the prior art to be solved by the present invention are that the high-dimensional geomagnetic coupling power generation system is not easy to implement with a circuit, and the circuit is unreliable.
发明内容SUMMARY OF THE INVENTION
本发明的目的是提供一种四维耦合发电超混沌系统模拟电路，其系统具有较强的混沌特性等。The purpose of the present invention is to provide a four-dimensional coupled power generation super-chaotic system analog circuit, the system of which has strong chaotic characteristics and the like.
为了达到上述目的，本发明采取的技术方案为：In order to achieve the above object, the technical scheme adopted in the present invention is:
一种四维耦合发电超混沌系统模拟电路，包括第一通道、第二通道、第三通道与第四通道；A four-dimensional coupled power generation hyperchaotic system simulation circuit, comprising a first channel, a second channel, a third channel and a fourth channel;
所述的第一通道的输出端连接第一通道的第一输入端、第二通道的第一输入端和第三通道中乘法器A1的第一输入引脚；第一通道输出端的前一级输出端连接第二通道中的乘法器A2的第一输入引脚；The output end of the first channel is connected to the first input end of the first channel, the first input end of the second channel and the first input pin of the multiplier A1 in the third channel; the previous stage of the output end of the first channel The output end is connected to the first input pin of the multiplier A2 in the second channel;
所述的第二通道的输出端连接第二通道的第二输入端、第四通道的输入端；第二通道输出端的前一级输出端连接第一通道的第二输入端、第一通道中乘法器A3的第一输入引脚和第三通道中乘法器A1的第二输入引脚；The output end of the second channel is connected to the second input end of the second channel and the input end of the fourth channel; the output end of the previous stage of the second channel output end is connected to the second input end of the first channel and the first channel The first input pin of the multiplier A3 and the second input pin of the multiplier A1 in the third channel;
所述的第三通道输出端的前一级输出端连接第一通道中乘法器 A3的第二输入引脚、第二通道的乘法器A2的第二输入引脚和第三通道的输入端；The output end of the previous stage of the output end of the third channel is connected to the second input pin of the multiplier A3 in the first channel, the second input pin of the multiplier A2 of the second channel and the input end of the third channel;
所述的第四通道输出端的前一级输出端连接第一通道的第三输入端。The output end of the previous stage of the output end of the fourth channel is connected to the third input end of the first channel.
所述的第一通道包括反相器U1，反相器U1的2引脚连接电阻R11、电阻R12、电阻R13，电阻R14和电阻R17的一端，电阻R11的另一端连接乘法器A3的输出端，电阻R12的另一端连接第一通道的输出端，电阻R13连接第二通道输出端的前一级输出端，电阻R14的另一端连接第四通道输出端的前一级输出端，电阻R17的另一端连接反相器U1 的6引脚和电阻R18的一端，电阻R18的另一端连接反相积分器U3的2 引脚和电容C1一端，电容C1另一端连接反相积分器U3的6引脚和电阻 R19的一端，电阻R19的另一端连接反相器U2的2引脚和电阻R20的一端，电阻R20的另一端连接反相器U2的6引脚；反相器U1的4引脚、反相器U2的4引脚与反相积分器U3的4引脚接VDD(负电压)，反相器 U1的7引脚、反相器U2的7引脚与反相积分器U3的7引脚接VCC(正电压)。The first channel includes an inverter U1, the 2 pins of the inverter U1 are connected to one end of the resistor R11, the resistor R12, the resistor R13, the resistor R14 and the resistor R17, and the other end of the resistor R11 is connected to the output of the multiplier A3. , the other end of the resistor R12 is connected to the output end of the first channel, the other end of the resistor R13 is connected to the output end of the previous stage of the output end of the second channel, the other end of the resistor R14 is connected to the output end of the previous stage of the output end of the fourth channel, and the other end of the resistor R17 Connect the 6-pin of the inverter U1 and one end of the resistor R18, the other end of the resistor R18 is connected to the 2-pin of the inverting integrator U3 and one end of the capacitor C1, and the other end of the capacitor C1 is connected to the 6-pin of the inverting integrator U3 and One end of the resistor R19, the other end of the resistor R19 is connected to the 2 pin of the inverter U2 and one end of the resistor R20, and the other end of the resistor R20 is connected to the 6 pin of the inverter U2; The 4-pin of the inverter U2 and the 4-pin of the inverting integrator U3 are connected to VDD (negative voltage), the 7-pin of the inverter U1, the 7-pin of the inverter U2 and the 7-pin of the inverting integrator U3 are connected. The pin is connected to VCC (positive voltage).
所述的第一通道的反相器U2的输出端是信号-x，反相积分器U3 的输出端是信号x。The output terminal of the inverter U2 of the first channel is the signal -x, and the output terminal of the inverting integrator U3 is the signal x.
所述的第二通道包括反相器U4，反相器U4的2引脚连接电阻R21、电阻R22、电阻R23与电阻R24的一端，电阻R21的另一端连接乘法器A2 的输出端，电阻R22的另一端连接第一通道的的输出端，电阻R23的另一端连接第二通道的输出端，电阻R24的另一端连接反相器U4的6引脚和电阻R25的一端，电阻R25的另一端连接反相积分器U6的2引脚和电容C2的一端，电容C2的另一端连接反相积分器U6的6引脚和电阻R26 的一端，电阻R26的另一端连接反相器U5的2引脚和电阻R27一端，电阻R27的另一端连接反相器U5的6引脚；反相放大器U4的3引脚、反相放大器U5的3引脚与反相积分器U6的3引脚接地；反相器U4的4引脚、反相器U5的4引脚与反相积分器U6的4引脚接VDD(负电压)，反相器U4 的7引脚、反相器U5的7引脚与反相积分器U6的7引脚接VCC(正电压)；The second channel includes an inverter U4, the 2 pins of the inverter U4 are connected to one end of the resistor R21, the resistor R22, the resistor R23 and the resistor R24, the other end of the resistor R21 is connected to the output of the multiplier A2, and the resistor R22 The other end of the resistor R23 is connected to the output end of the first channel, the other end of the resistor R23 is connected to the output end of the second channel, the other end of the resistor R24 is connected to the 6 pin of the inverter U4 and one end of the resistor R25, and the other end of the resistor R25 Connect the 2-pin of the inverting integrator U6 and one end of the capacitor C2, the other end of the capacitor C2 is connected to the 6-pin of the inverting integrator U6 and one end of the resistor R26, and the other end of the resistor R26 is connected to the 2-pin of the inverter U5. The pin and one end of the resistor R27, the other end of the resistor R27 is connected to the 6-pin of the inverter U5; the 3-pin of the inverting amplifier U4, the 3-pin of the inverting amplifier U5 and the 3-pin of the inverting integrator U6 are grounded; The 4-pin of the inverter U4, the 4-pin of the inverter U5 and the 4-pin of the inverting integrator U6 are connected to VDD (negative voltage), the 7-pin of the inverter U4, the 7-pin of the inverter U5 The pin and the 7 pin of the inverting integrator U6 are connected to VCC (positive voltage);
所述的第二通道反相器U5的输出端信号是-y，第二通道反相积分器U6的输出端是信号y。The output terminal of the second channel inverter U5 is -y, and the output terminal of the second channel inverting integrator U6 is the signal y.
所述的第三通道包括反相器U7，反相器U7的2脚本连接电阻 R31、电阻R32和电阻R34的一端，电阻R31的另一端连接乘法器 A1输出端，电阻R32的另一端连接第三通道输出端的前一级输出端，电阻R34的另一端连接反相器U7的6引脚和电阻R35一端，电阻R35另一端连接电容C3的一端和反相积分器U9的引脚2，电容C3 的另一端连接反相积分器U9的6引脚和电阻R36的一端，电阻R36 另一端连接电阻R38一端和反相器U8的2引脚，电阻R38另一端连接反相器U8的6引脚；反相放大器U7的3引脚、反相放大器U8 的3引脚与反相积分器U9的3引脚接地；反相器U7的4引脚、反相器U8的4引脚与反相积分器U9的4引脚接VDD(负电压)，反相器U7的7引脚、反相器U8的7引脚与反相积分器U9的7引脚接VCC(正电压)。The third channel includes an inverter U7, the second end of the inverter U7 is connected to one end of the resistor R31, the resistor R32 and the resistor R34, the other end of the resistor R31 is connected to the output of the multiplier A1, and the other end of the resistor R32 is connected to the first end. The output terminal of the previous stage of the three-channel output terminal, the other end of the resistor R34 is connected to the 6 pin of the inverter U7 and one end of the resistor R35, the other end of the resistor R35 is connected to one end of the capacitor C3 and the
所述的第三通道反相器U8的输出端信号是-z，第三通道反相积分器U9的输出端是信号z。The output terminal of the third channel inverter U8 is -z, and the output terminal of the third channel inverting integrator U9 is the signal z.
所述的第四通道包括反相器U10，反相器U10的2脚本连接电阻R41和电阻R43的一端，电阻R41的另一端连接第二通道的输出端，电阻R43的另一端连接反相器U10的引脚6和电阻R44的一端，电阻R44的另一端连接电容C4的一端和反相积分器U12的2引脚，电容C4的另一端连接反相积分器U12的6引脚和电阻R45的一端，电阻R45的另一端连接电阻R47一端和反相器U11的2引脚，电阻 R47的另一端连接反相器U11的6引脚；反相器U10的3引脚、反相器U11的3引脚接地与反相积分器U12的3引脚接地；反相器U10 的4引脚、反相器U11的4引脚以及反相积分器U12的4引脚接VDD (负电压)，反相器U10的7引脚、反相器U11的7引脚以及反相器积分U12的7引脚接VCC(正电压)。The fourth channel includes an inverter U10, the second end of the inverter U10 is connected to one end of the resistor R41 and the resistor R43, the other end of the resistor R41 is connected to the output end of the second channel, and the other end of the resistor R43 is connected to the inverter. Pin 6 of U10 and one end of resistor R44, the other end of resistor R44 is connected to one end of capacitor C4 and
所述的第四通道反相器U11的输出端信号是-w，第四通道反相积分器U12的输出端是信号w。The output terminal signal of the fourth channel inverter U11 is -w, and the output terminal of the fourth channel inverting integrator U12 is the signal w.
所述的反相器U1、反相器U2、反相积分器U3、反相器U4、反相器U5、反相积分器U6、反相器U7、反相器U8、反相积分器U9、反相器U10、反相器U11以及反相积分器U12采用运放器LM741。Described inverter U1, inverter U2, inverting integrator U3, inverter U4, inverter U5, inverting integrator U6, inverter U7, inverter U8, inverting integrator U9 , the inverter U10, the inverter U11 and the inverting integrator U12 use the operational amplifier LM741.
所述的乘法器A1、乘法器A2与乘法器A3采用乘法器AD633。The multiplier A1, the multiplier A2 and the multiplier A3 use the multiplier AD633.
所述的第一通道中电阻R11＝1kΩ，电阻R12＝33kΩ，电阻 R13＝1KΩ，电阻R16＝10KΩ，电阻R17＝10KΩ，电阻R18＝10KΩ，电阻R14＝1KΩ，电阻R19＝1KΩ，电阻R20＝1KΩ，电容C1＝10nF；第二通道中电阻R21＝0.5KΩ，电阻R22＝3.3KΩ，电阻R23＝10KΩ，电阻R24＝10KΩ，电阻R25＝10KΩ，电阻R26＝10KΩ,电阻R27＝10KΩ,电容C2＝0.1μF；第三通道中电阻R31＝1KΩ，电阻R32＝10KΩ，电阻 R34＝1KΩ，电阻R35＝5KΩ，电阻R36＝10KΩ，电阻R38＝10KΩ，电容C3＝10nF；第四通道中电阻R41＝5KΩ，电阻R43＝10KΩ，电阻 R44＝10KΩ，电阻R45＝10KΩ，电阻R47＝10KΩ,电容C4＝10nF； VCC＝15V，VDD＝-15V。In the first channel, resistor R11=1kΩ, resistor R12=33kΩ, resistor R13=1KΩ, resistor R16=10KΩ, resistor R17=10KΩ, resistor R18=10KΩ, resistor R14=1KΩ, resistor R19=1KΩ, resistor R20= 1KΩ, capacitor C1=10nF; in the second channel, resistor R21=0.5KΩ, resistor R22=3.3KΩ, resistor R23=10KΩ, resistor R24=10KΩ, resistor R25=10KΩ, resistor R26=10KΩ, resistor R27=10KΩ, capacitor C2 =0.1μF; in the third channel, resistance R31 = 1KΩ, resistance R32 = 10KΩ, resistance R34 = 1KΩ, resistance R35 = 5KΩ, resistance R36 = 10KΩ, resistance R38 = 10KΩ, capacitor C3 = 10nF; in the fourth channel, resistance R41 = 5KΩ, resistor R43=10KΩ, resistor R44=10KΩ, resistor R45=10KΩ, resistor R47=10KΩ, capacitor C4=10nF; VCC=15V, VDD=-15V.
本发明的有益效果：Beneficial effects of the present invention:
本发明的模拟示波器上易观察出x-y，x-z，y-z，x-w，y-w，z-w 相图，具有电路结构较为简单，易实现，适用于非线性混沌电路的教学与演示以及耦合发电系统模型分析研究。The analog oscilloscope of the present invention can easily observe x-y, x-z, y-z, x-w, y-w, z-w phase diagrams, has a relatively simple circuit structure, is easy to implement, and is suitable for teaching and demonstration of nonlinear chaotic circuits and analysis and research of coupled power generation system models.
附图说明Description of drawings
图1是本发明的电路图。FIG. 1 is a circuit diagram of the present invention.
图2是图1的x输出波形图。FIG. 2 is an x-output waveform diagram of FIG. 1 .
图3是图1的y输出波形图。FIG. 3 is a y output waveform diagram of FIG. 1 .
图4是图1的z输出波形图。FIG. 4 is a z output waveform diagram of FIG. 1 .
图5是图1的w输出波形图。FIG. 5 is a w output waveform diagram of FIG. 1 .
图6是图1的x-y输出相图。FIG. 6 is an x-y output phase diagram of FIG. 1 .
图7是图1的x-z输出相图。FIG. 7 is an x-z output phase diagram of FIG. 1 .
图8是图1的y-z输出相图。FIG. 8 is a y-z output phase diagram of FIG. 1 .
图9是图1的x-w输出相图。FIG. 9 is an x-w output phase diagram of FIG. 1 .
图10是图1的y-w输出相图。FIG. 10 is a y-w output phase diagram of FIG. 1 .
图11是图1的z-w输出相图。FIG. 11 is a z-w output phase diagram of FIG. 1 .
具体实施方式Detailed ways
下面结合附图和实施例对本发明做详细描述。The present invention will be described in detail below with reference to the accompanying drawings and embodiments.
参照图1，一种四维耦合发电超混沌系统模拟电路，包括第一通道、第二通道、第三通道与第四通道；1, a four-dimensional coupled power generation hyperchaotic system simulation circuit, including a first channel, a second channel, a third channel and a fourth channel;
所述的第一通道的输出端连接第一通道的第一输入端、第二通道的第一输入端和接第三通道中乘法器A1的第一输入引脚；第一通道输出端的前一级输出端连接第二通道中的乘法器A2的第一输入引脚；The output end of the first channel is connected to the first input end of the first channel, the first input end of the second channel and the first input pin of the multiplier A1 in the third channel; The stage output is connected to the first input pin of the multiplier A2 in the second channel;
所述的第二通道的输出端连接第二通道的第二输入端、第四通道的输入端；第二通道输出端的前一级输出端连接第一通道的第二输入端、第一通道中乘法器A3的第一输入引脚和第三通道中乘法器A1的第二输入引脚；The output end of the second channel is connected to the second input end of the second channel and the input end of the fourth channel; the output end of the previous stage of the second channel output end is connected to the second input end of the first channel and the first channel The first input pin of the multiplier A3 and the second input pin of the multiplier A1 in the third channel;
所述的第三通道输出端的前一级输出端连接第一通道中乘法器 A3的第二输入引脚、第二通道的乘法器A2的第二输入引脚和第三通道的输入端；The output end of the previous stage of the output end of the third channel is connected to the second input pin of the multiplier A3 in the first channel, the second input pin of the multiplier A2 of the second channel and the input end of the third channel;
所述的第四通道输出端的前一级输出端连接第一通道的第三输入端。The output end of the previous stage of the output end of the fourth channel is connected to the third input end of the first channel.
所述的第一通道包括反相器U1，反相器U1的2引脚连接电阻R11、电阻R12、电阻R13，电阻R14和电阻R17的一端，电阻R11的另一端连接乘法器A3的输出端，电阻R12的另一端连接第一通道的输出端，电阻R13连接第二通道输出端的前一级输出端，电阻R14第四通道输出端的前一级输出端，电阻R17的另一端连接反相器U1的6引脚和电阻R18的一端，电阻R18的另一端连接反相积分器U3的2引脚和电容 C1一端，电容C1另一端连接反相积分器U3的6引脚和电阻R19的一端，电阻R19的另一端连接反相器U2的2引脚和电阻R20的一端，电阻R20 的另一端连接反相器U2的6引脚；反相器U1的4引脚、反相器U2的4 引脚与反相积分器U3的4引脚接VDD(负电压)，反相器U1的7引脚、反相器U2的7引脚与反相积分器U3的7引脚接VCC(正电压)。The first channel includes an inverter U1, the 2 pins of the inverter U1 are connected to one end of the resistor R11, the resistor R12, the resistor R13, the resistor R14 and the resistor R17, and the other end of the resistor R11 is connected to the output of the multiplier A3. , the other end of the resistor R12 is connected to the output end of the first channel, the other end of the resistor R13 is connected to the output end of the previous stage of the output end of the second channel, the other end of the resistor R14 is connected to the output end of the previous stage of the output end of the fourth channel, and the other end of the resistor R17 is connected to the inverter Pin 6 of U1 and one end of resistor R18, the other end of resistor R18 is connected to
所述的第一通道的反相器U2的输出端是信号-x，反相积分器U3 的输出端是信号x。The output terminal of the inverter U2 of the first channel is the signal -x, and the output terminal of the inverting integrator U3 is the signal x.
所述的第二通道包括反相器U4，反相器U4的2引脚连接电阻R21、电阻R22、电阻R23与电阻R24的一端，电阻R21的另一端连接乘法器A2 的输出端，电阻R22的另一端连接第一通道的的输出端，电阻R23的一端连接第二通道的输出端，电阻R24的另一端连接反相器U4的6引脚和电阻R25的一端，电阻R25的另一端连接反相积分器U6的2引脚和电容 C2的一端，电容C2的另一端连接反相积分器U6的6引脚和电阻R26的一端，电阻R26的另一端连接反相器U5的2和电阻R27一端，电阻R27的另一端连接反相器U5的6引脚；反相放大器U4的3引脚、反相放大器U5 的3引脚与反相积分器U6的3引脚接地；反相器U4的4引脚、反相器U5 的4引脚与反相积分器U6的4引脚接VDD(负电压)，反相器U4的7引脚、反相器U5的7引脚与反相积分器U6的7引脚接VCC(正电压)；The second channel includes an inverter U4, the 2 pins of the inverter U4 are connected to one end of the resistor R21, the resistor R22, the resistor R23 and the resistor R24, the other end of the resistor R21 is connected to the output of the multiplier A2, and the resistor R22 The other end of the resistor R23 is connected to the output end of the first channel, one end of the resistor R23 is connected to the output end of the second channel, the other end of the resistor R24 is connected to the 6 pin of the inverter U4 and one end of the resistor R25, and the other end of the resistor R25 is connected
所述的第二通道反相器U5的输出端信号是-y，第二通道反相积分器U6的输出端是信号y。The output terminal of the second channel inverter U5 is -y, and the output terminal of the second channel inverting integrator U6 is the signal y.
所述的第三通道包括反相器U7，反相器U7的2脚本连接电阻 R31、电阻R32和电阻R34的一端，电阻R31的另一端连接乘法器 A1输出端，电阻R32的另一端连接第三通道输出端的前一级输出端，电阻R34的另一端连接反相器U7的6引脚和电阻R35一端，电阻 R35另一端连接电容C3的一端和反相积分器U9的引脚2，电容C3 的另一端连接反相积分器U9的6引脚和电阻R36的一端，电阻R36 另一端连接电阻R38一端和反相器U8的2引脚，电阻R38另一端连接反相器U8的6引脚；反相放大器U7的3引脚、反相放大器U8 的3引脚与反相积分器U9的3引脚接地；反相器U7的4引脚、反相器U8的4引脚与反相积分器U9的4引脚接VDD(负电压)，反相器U7的7引脚、反相器U8的7引脚与反相积分器U9的7引脚接VCC(正电压)。The third channel includes an inverter U7, the second end of the inverter U7 is connected to one end of the resistor R31, the resistor R32 and the resistor R34, the other end of the resistor R31 is connected to the output of the multiplier A1, and the other end of the resistor R32 is connected to the first end. The output terminal of the previous stage of the three-channel output terminal, the other end of the resistor R34 is connected to the 6 pin of the inverter U7 and one end of the resistor R35, the other end of the resistor R35 is connected to one end of the capacitor C3 and the
所述的第三通道反相器U8的输出端信号是-z，第三通道反相积分器U9的输出端是信号z。The output terminal of the third channel inverter U8 is -z, and the output terminal of the third channel inverting integrator U9 is the signal z.
所述的第四通道包括反相器U10，反相器U10的2脚本连接电阻R41和电阻R43的一端，电阻R41的另一端连接第二通道的输出端，电阻R43的另一端连接反相器U10的引脚6和电阻R44的一端，电阻R44的另一端连接电容C4的一端和反相积分器U12的2引脚，电容C4的另一端连接反相积分器U12的6引脚和电阻R45的一端，电阻R45的另一端连接电阻R47一端和反相器U11的2引脚，电阻 R47的另一端连接反相器U11的6引脚；反相器U10的3引脚、反相器U11的3引脚接地与反相积分器U12的3引脚接地；反相器U10 的4引脚、反相器U11的4引脚以及反相积分器U12的4引脚接VDD (负电压)，反相器U10的7引脚、反相器U11的7引脚以及反相器积分U12的7引脚接VCC(正电压)。The fourth channel includes an inverter U10, the second end of the inverter U10 is connected to one end of the resistor R41 and the resistor R43, the other end of the resistor R41 is connected to the output end of the second channel, and the other end of the resistor R43 is connected to the inverter. Pin 6 of U10 and one end of resistor R44, the other end of resistor R44 is connected to one end of capacitor C4 and
所述的第四通道反相器U11的输出端信号是-w，第四通道反相积分器U12的输出端是信号w。The output terminal signal of the fourth channel inverter U11 is -w, and the output terminal of the fourth channel inverting integrator U12 is the signal w.
所述的反相器U1、反相器U2、反相积分器U3、反相器U4、反相器U5、反相积分器U6、反相器U7、反相器U8、反相积分器U9、反相器U10、反相器U11以及反相积分器U12采用运放器LM741。Described inverter U1, inverter U2, inverting integrator U3, inverter U4, inverter U5, inverting integrator U6, inverter U7, inverter U8, inverting integrator U9 , the inverter U10, the inverter U11 and the inverting integrator U12 use the operational amplifier LM741.
所述的乘法器A1、乘法器A2与乘法器A3采用乘法器AD633。The multiplier A1, the multiplier A2 and the multiplier A3 use the multiplier AD633.
所述的第一通道中电阻R11＝1kΩ，电阻R12＝33kΩ，电阻 R13＝1KΩ，电阻R16＝10KΩ，电阻R17＝10KΩ，电阻R18＝10KΩ，电阻R14＝1KΩ，电阻R19＝1KΩ，电阻R20＝1KΩ，电容C1＝10nF；第二通道中电阻R21＝0.5KΩ，电阻R22＝3.3KΩ，电阻R23＝10KΩ，电阻R24＝10KΩ，电阻R25＝10KΩ，电阻R26＝10KΩ,电阻R27＝10KΩ,电容C2＝0.1μF；第三通道中电阻R31＝1KΩ，电阻R32＝10KΩ，电阻R34＝1KΩ，电阻R35＝5KΩ，电阻R36＝10KΩ，电阻R38＝10KΩ，电容C3＝10nF；第四通道中电阻R41＝5KΩ，电阻R43＝10KΩ，电阻 R44＝10KΩ，电阻R45＝10KΩ，电阻R47＝10KΩ,电容C4＝10nF； VCC＝15V，VDD＝-15V。In the first channel, resistor R11=1kΩ, resistor R12=33kΩ, resistor R13=1KΩ, resistor R16=10KΩ, resistor R17=10KΩ, resistor R18=10KΩ, resistor R14=1KΩ, resistor R19=1KΩ, resistor R20= 1KΩ, capacitor C1=10nF; in the second channel, resistor R21=0.5KΩ, resistor R22=3.3KΩ, resistor R23=10KΩ, resistor R24=10KΩ, resistor R25=10KΩ, resistor R26=10KΩ, resistor R27=10KΩ, capacitor C2 =0.1μF; in the third channel, resistance R31 = 1KΩ, resistance R32 = 10KΩ, resistance R34 = 1KΩ, resistance R35 = 5KΩ, resistance R36 = 10KΩ, resistance R38 = 10KΩ, capacitor C3 = 10nF; in the fourth channel, resistance R41 = 5KΩ, resistor R43=10KΩ, resistor R44=10KΩ, resistor R45=10KΩ, resistor R47=10KΩ, capacitor C4=10nF; VCC=15V, VDD=-15V.
本发明的工作原理为：The working principle of the present invention is:
本发明涉及的四维耦合发电超混沌系统，因该系统含有两个李雅普诺夫指数大于0，故使得该电路的混沌特性十分复杂。如果将该电路的输出信号作为载波信号，与目标信号通过相关算法调制，即可到达通信保密的效果。本发明涉及的无量纲数学模型如下：The four-dimensional coupled power generation super-chaotic system involved in the present invention has two Lyapunov exponents greater than 0, so the chaotic characteristics of the circuit are very complicated. If the output signal of the circuit is used as a carrier signal and modulated with the target signal through a correlation algorithm, the effect of communication security can be achieved. The dimensionless mathematical model involved in the present invention is as follows:
式(1)中，x,y,z,w为状态变量，α,b,c,k为方程的参数。系统(1) 即四维耦合发电超混沌系统。In formula (1), x, y, z, w are state variables, and α, b, c, and k are parameters of the equation. System (1) is a four-dimensional coupled power generation hyperchaotic system.
本发明所涉及的电路由第一、第二、第三，第四通道的电路组成，第一、第二、第三、第四通道的电路分别实现了式(1)中的第一、第二、第三，第四函数。反相积分器与反相器采用LM741，模拟乘法器采用AD633时，电路的输出波形图见图2、图3、图4, 图5，电路输出的相图见图6、图7、图8、图9、图10、图11，图2 至图11反映出了四维耦合发电系统的基本混沌特性，从而丰富了混沌的类型，为混沌系统为描述地磁极性反转提供了新的模型与思路。The circuit involved in the present invention is composed of circuits of the first, second, third, and fourth channels, and the circuits of the first, second, third, and fourth channels respectively realize the first and the fourth channel in the formula (1). Second, third, and fourth functions. When the inverting integrator and inverter use LM741, and the analog multiplier uses AD633, the output waveform diagram of the circuit is shown in Figure 2, Figure 3, Figure 4, and Figure 5, and the phase diagram of the circuit output is shown in Figure 6, Figure 7, and Figure 8 , Figure 9, Figure 10, Figure 11, Figure 2 to Figure 11 reflect the basic chaotic characteristics of the four-dimensional coupled power generation system, thus enriching the types of chaos, and providing a new model for the chaotic system to describe the geomagnetic polarity reversal. ideas.
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