CN101510862A - Method and system for generating ultra-chaos signal - Google Patents
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Abstract
本发明涉及保密通信技术领域,具体涉及一种超混沌信号的发生方法和发生系统;其中超混沌信号发生方法,包括如下步骤:输入正弦信号到能产生混沌信号的非线性电路,从而改变所述能产生混沌信号的非线性电路的状态方程参数,使混沌系统的李亚普诺夫指数至少有2个大于0;超混沌信号发生系统,包括能产生混沌信号的非线性电路,所述超混沌信号发生系统还包括正弦信号发生装置,所述正弦信号发生装置与所述能产生混沌信号的非线性电路的信号输入端连接,所述正弦信号发生装置输出正弦信号到所述能产生混沌信号的非线性电路,从而改变所述能产生混沌信号的非线性电路的状态方程参数,使混沌系统的李亚普诺夫指数至少有2个大于0。
The present invention relates to the technical field of secure communication, in particular to a generation method and generation system of a hyperchaotic signal; wherein the hyperchaotic signal generation method includes the following steps: input a sinusoidal signal to a nonlinear circuit capable of generating a chaotic signal, thereby changing the The parameters of the state equation of the nonlinear circuit that can generate chaotic signals, so that at least two of the Lyapunov exponents of the chaotic system are greater than 0; The system also includes a sinusoidal signal generating device, the sinusoidal signal generating device is connected to the signal input end of the nonlinear circuit capable of generating chaotic signals, and the sinusoidal signal generating device outputs a sinusoidal signal to the nonlinear circuit capable of generating chaotic signals circuit, thereby changing the parameters of the state equation of the nonlinear circuit capable of generating chaotic signals, so that at least two of the Lyapunov exponents of the chaotic system are greater than 0.
Description
技术领域 technical field
本发明涉及保密通信技术领域,具体涉及一种超混沌信号的发生方法和发生系统。The invention relates to the technical field of secure communication, in particular to a method and system for generating hyperchaotic signals.
背景技术 Background technique
自1963年Lorenz(洛伦兹)发现第一个混沌模型以来,混沌动力学在非线性研究领域取得了重大发展。Since the discovery of the first chaotic model by Lorenz in 1963, chaotic dynamics has achieved significant development in the field of nonlinear research.
混沌之所以可以用于数字信息加密是因为混沌运动有以下特点:1)运动轨迹对初始值极其敏感,在任意接近的两点出发的轨迹不可预测;2)混沌运动既非周期又不收敛,运动轨迹上的点遍历整个区域;3)运动轨迹在有限区域内不断伸缩折叠使系统输出类似随机噪声的现象。但对于普通混沌系统而言,超混沌系统具有两个及其以上正的Lyapunov(李亚普诺夫)指数,其性质更复杂,所以,超混沌信号作为混沌加密信号具有更广泛的应用前景。The reason why chaos can be used for digital information encryption is that the chaotic motion has the following characteristics: 1) The trajectory of the motion is extremely sensitive to the initial value, and the trajectory starting from any two points close to it is unpredictable; 2) The chaotic motion is neither periodic nor convergent. The points on the motion trajectory traverse the entire area; 3) The continuous expansion and folding of the motion trajectory in a limited area makes the system output a phenomenon similar to random noise. But for the ordinary chaotic system, the hyperchaotic system has two or more positive Lyapunov (Lyapunov) exponents, and its properties are more complex. Therefore, the hyperchaotic signal has a wider application prospect as a chaotic encrypted signal.
但现在都是通过添加一个含有电位器的状态反馈控制器施加于连续混沌系统从而获得超混沌,这样不但使电路系统更为复杂,而且调节电位器很容易过调或者欠调,使实际得到的阻值与理想的阻值存在一定的误差。But now, super-chaos is obtained by adding a state feedback controller containing a potentiometer to the continuous chaotic system, which not only makes the circuit system more complicated, but also adjusts the potentiometer to easily overshoot or undershoot, making the actual obtained There is a certain error between the resistance value and the ideal resistance value.
如公开号为CN25433620Y的中国发明专利申请公布说明书提供了一种数字混沌的产生方法,其是通过设定计算的初值和方程来产生混沌信号,但不能产生超混沌信号,也不能随时改变输出信号。而公开号为CN101145901A的中国发明专利申请公布说明书提供了一种超混沌的产生方法,但它只能在固定的超混沌映射方程产生超混沌,而且只有通过设定不同的初值来改变超混沌输出,不能起到控制超混沌系统的目的。For example, the Chinese invention patent application publication with the publication number CN25433620Y provides a method for generating digital chaos, which generates a chaotic signal by setting the initial value and equation for calculation, but cannot generate a super chaotic signal, nor can it change the output at any time Signal. And publication number is that the Chinese invention patent application announcement specification of CN101145901A provides a kind of generation method of hyperchaos, but it can only produce hyperchaos in fixed hyperchaos mapping equation, and only changes hyperchaos by setting different initial values The output cannot serve the purpose of controlling the hyperchaotic system.
发明内容 Contents of the invention
有鉴于此,为了解决上述问题,本发明提供一种不用添加新的状态变量的超混沌信号发生方法。In view of this, in order to solve the above problems, the present invention provides a hyperchaotic signal generation method without adding new state variables.
本发明的目的是这样实现的,超混沌信号发生方法,包括如下步骤:输入正弦信号到能产生混沌信号的非线性电路,从而改变所述能产生混沌信号的非线性电路的状态方程参数,使混沌系统的李亚普诺夫指数至少有2个大于0。The object of the present invention is achieved like this, super chaotic signal generating method, comprises the steps: input sinusoidal signal to the non-linear circuit that can produce chaotic signal, thereby change the state equation parameter of described non-linear circuit that can produce chaotic signal, make At least two of the Lyapunov exponents of the chaotic system are greater than 0.
进一步,所述正弦信号是由单片正弦信号发生芯片或RC振荡电路产生的;Further, the sinusoidal signal is generated by a single-chip sinusoidal signal generation chip or an RC oscillator circuit;
进一步,所述正弦信号通过电位器或乘法器输入能产生混沌信号的非线性电路。Further, the sinusoidal signal is input into a nonlinear circuit capable of generating chaotic signals through a potentiometer or a multiplier.
本发明还提供一种超混沌信号发生系统,包括能产生混沌信号的非线性电路,所述超混沌信号发生系统还包括正弦信号发生装置,所述正弦信号发生装置与所述能产生混沌信号的非线性电路的信号输入端连接,所述正弦信号发生装置输出正弦信号到所述能产生混沌信号的非线性电路,从而改变所述能产生混沌信号的非线性电路的状态方程参数,使混沌系统的李亚普诺夫指数至少有2个大于0。The present invention also provides a hyperchaotic signal generating system, including a nonlinear circuit capable of generating chaotic signals, the hyperchaotic signal generating system also includes a sinusoidal signal generating device, the sinusoidal signal generating device and the chaotic signal generating device The signal input end of the nonlinear circuit is connected, and the sinusoidal signal generating device outputs a sinusoidal signal to the nonlinear circuit that can generate chaotic signals, thereby changing the state equation parameters of the nonlinear circuit that can generate chaotic signals, so that the chaotic system At least 2 of the Lyapunov exponents are greater than 0.
进一步,所述正弦信号发生装置为单片正弦信号发生芯片或RC振荡电路;Further, the sinusoidal signal generating device is a single-chip sinusoidal signal generation chip or an RC oscillator circuit;
进一步,所述正弦信号发生装置通过电位器或乘法器与能产生混沌信号的非线性电路的信号输入端连接;Further, the sinusoidal signal generating device is connected to the signal input end of the nonlinear circuit capable of generating chaotic signals through a potentiometer or a multiplier;
进一步,所述能产生混沌信号的非线性电路由参数设置模块、积分模块、反馈模块、供电模块和输出模块构成;所述参数设置模块用于设置电路系统的参数;所述积分模块对参数设置模块输出电信号进行积分处理;所述反馈模块将积分模块输出的电信号反馈到参数设置模块的输入端;供电模块对参数设置模块和积分模块进行供电;所述输出模块作为系统的输出。Further, the nonlinear circuit capable of generating chaotic signals is composed of a parameter setting module, an integration module, a feedback module, a power supply module and an output module; the parameter setting module is used to set the parameters of the circuit system; the parameter setting module of the integration module The module outputs electrical signals for integration processing; the feedback module feeds back the electrical signals output by the integration module to the input of the parameter setting module; the power supply module supplies power to the parameter setting module and the integration module; the output module serves as the output of the system.
本发明的超混沌信号发生方法和超混沌信号发生系统,通过输入正弦信号到非线性电路,改变非线性电路的状态方程参数,从而改变电路系统状态方程的雅可比矩阵,使系统方程的Lyapunov指数有两个大于0,从而使电路系统达到超混沌系统状态,由于不用添加一个新的状态变量,从而实现起来更为简单,也不增加原系统的复杂度,相比现有技术中调节电位器,更容易得到理想的参数;此外,通过调节输入的正弦信号频率,本发明超混沌信号发生系统可方便地在混沌与超混沌状态,以及不同超混沌状态间转换。The hyperchaotic signal generating method and hyperchaotic signal generating system of the present invention change the state equation parameters of the nonlinear circuit by inputting sinusoidal signals to the nonlinear circuit, thereby changing the Jacobian matrix of the circuit system state equation and making the Lyapunov exponent of the system equation There are two greater than 0, so that the circuit system reaches the state of a super-chaotic system. Since there is no need to add a new state variable, it is simpler to implement and does not increase the complexity of the original system. Compared with the adjustment of the potentiometer in the prior art , it is easier to obtain ideal parameters; in addition, by adjusting the frequency of the input sinusoidal signal, the hyperchaotic signal generating system of the present invention can conveniently switch between chaotic and hyperchaotic states, and between different hyperchaotic states.
本发明的其他优点、目标,和特征在某种程度上将在随后的说明书中进行阐述,并且在某种程度上,基于对下文的考察研究对本领域技术人员而言将是显而易见的,或者可以从本发明的实践中得到教导。本发明的目标和其他优点可以通过下面的说明书,权利要求书,以及附图中所特别指出的结构来实现和获得。Other advantages, objects, and features of the present invention will be set forth in the ensuing description to some extent, and to some extent, will be obvious to those skilled in the art based on the investigation and research below, or can be Learn from the practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
附图说明 Description of drawings
为了使本发明的目的、技术方案和优点更加清楚,下面将结合附图对本发明作进一步的详细描述:In order to make the purpose of the present invention, technical solutions and advantages clearer, the present invention will be described in further detail below in conjunction with accompanying drawing:
图1示出了本发明超混沌信号发生系统的功能模块示意图;Fig. 1 shows the functional module schematic diagram of hyperchaotic signal generating system of the present invention;
图2示出了实施例1加入正弦信号发生装置之前的非线性电路示意图;Fig. 2 shows the schematic diagram of the non-linear circuit before adding the sinusoidal signal generating device in
图3示出了实施例1加入正弦信号发生装置之前的非线性电路示意图;Fig. 3 shows the schematic diagram of the non-linear circuit before adding the sinusoidal signal generating device in
图4示出了实施例1的超混沌系统的Lyapunov指数谱;Fig. 4 shows the Lyapunov exponent spectrum of the hyperchaotic system of
图5示出了实施例2的超混沌系统的Lyapunov指数谱;Fig. 5 shows the Lyapunov exponent spectrum of the hyperchaotic system of
图6示出了实施例3的超混沌系统的Lyapunov指数谱。FIG. 6 shows the Lyapunov exponent spectrum of the hyperchaotic system in
具体实施方式 Detailed ways
以下将结合附图,对本发明的优选实施例进行详细的描述。Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
实施例1Example 1
本实施例的能产生混沌信号的非线性电路如图2所示,其系统方程为:The non-linear circuit that can produce chaotic signal of the present embodiment is as shown in Figure 2, and its system equation is:
此系统的Lyapunov指数为:LE1=2.7234,LE2=-0.0622,LE3=-16.6613。The Lyapunov exponents of this system are: LE1=2.7234, LE2=-0.0622, LE3=-16.6613.
如图2、图3所示,所述能产生混沌信号的非线性电路,由运算放大器、乘法器、电阻、电容构成,其中运算放大器LM1、LM4、LM7及其包括乘法器和电阻的外围电路共同构成参数设置模块,运算放大器LM2、LM5、LM8及其包括电容和电阻的外围电路共同构成积分模块,运算放大器LM3、LM6、LM9及其包括电容和电阻的外围电路共同构成反馈模块,其余三个运算放大器则构成输出模块,所述参数设置模块用于设置电路系统的参数;所述积分模块对参数设置模块输出电信号进行积分处理;所述反馈模块将积分模块输出的电信号反馈到参数设置模块的输入端,所述输出模块的输入端与反馈模块的输出端连接,防止输出端U1、U2、U3所连接的外围电路对反馈模块造成影响。其中运算放大器可选用LM741,乘法器可选用AD633JN,将正弦信号发生装置连接于该电路的第三个电路方程的非线形电路输入端,中间加一电位器,则构成一新的加法项,该项的系数由输入信号的幅值和电位器共同决定。As shown in Fig. 2 and Fig. 3, the nonlinear circuit capable of generating chaotic signals is composed of operational amplifiers, multipliers, resistors, and capacitors, wherein operational amplifiers LM1, LM4, LM7 and their peripheral circuits including multipliers and resistors Together constitute the parameter setting module, operational amplifiers LM2, LM5, LM8 and their peripheral circuits including capacitors and resistors together constitute an integral module, operational amplifiers LM3, LM6, LM9 and their peripheral circuits including capacitors and resistors jointly constitute a feedback module, and the remaining three An operational amplifier constitutes an output module, and the parameter setting module is used to set the parameters of the circuit system; the integral module performs integral processing on the output electric signal of the parameter setting module; the feedback module feeds back the electric signal output by the integral module to the parameter The input terminal of the module is set, and the input terminal of the output module is connected with the output terminal of the feedback module to prevent the peripheral circuits connected to the output terminals U 1 , U 2 , and U 3 from affecting the feedback module. Among them, the operational amplifier can choose LM741, the multiplier can choose AD633JN, connect the sinusoidal signal generating device to the nonlinear circuit input end of the third circuit equation of the circuit, and add a potentiometer in the middle to form a new addition term. The coefficient of the term is determined by the amplitude of the input signal and the potentiometer.
则原系统方程变为:Then the original system equation becomes:
选取a=1100为正弦函数的系数。Select a = 1100 as the coefficient of the sine function.
为方便计算,将系统方程改写成一四维自治系统:For the convenience of calculation, the system equation is rewritten as a four-dimensional autonomous system:
其中ω为输入信号的角频率,它和输入信号的频率满足ω=2πf。参见图4,混沌系统的Lyapunov指数谱可以看出,改变控制信号的频率,系统的动力学特征会发生改变。Where ω is the angular frequency of the input signal, which satisfies ω=2πf with the frequency of the input signal. Referring to Figure 4, the Lyapunov exponent spectrum of the chaotic system can be seen that changing the frequency of the control signal will change the dynamic characteristics of the system.
当控制信号的输入角频率为在ω=4.7,5.8,9.2和9.8也就是输入信号的频率在748Hz,923Hz,1.464KHz和1.599KHz时,此时系统的Lyapunov指数有两个大于0;此时本实施例产生的信号为超混沌信号。When the input angular frequency of the control signal is at ω=4.7, 5.8, 9.2 and 9.8, that is, the frequency of the input signal is at 748Hz, 923Hz, 1.464KHz and 1.599KHz, two of the Lyapunov exponents of the system are greater than 0 at this time; The signal generated in this embodiment is a hyperchaotic signal.
实施例2Example 2
本实施例的能产生混沌信号的非线性电路,其系统方程为:The non-linear circuit that can produce chaotic signal of the present embodiment, its system equation is:
此系统的Lyapunov指数为:LE1=2.7234,LE2=-0.0622,LE3=-16.6613The Lyapunov exponent of this system is: LE1=2.7234, LE2=-0.0622, LE3=-16.6613
将正弦信号发生装置连接于该电路的第二个电路方程的非线形电路输入端,通过一乘法器接入非线性电路,正弦信号与信号输入y一起输入非线形电路输入端,构成一新的乘法项,该项的系数由输入信号的幅值和电位器共同决定。Connect the sinusoidal signal generating device to the input end of the nonlinear circuit of the second circuit equation of the circuit, connect the nonlinear circuit through a multiplier, and input the sinusoidal signal and the signal input y to the input end of the nonlinear circuit together to form a new The multiplication item, the coefficient of which is determined by the amplitude of the input signal and the potentiometer.
则原系统方程变为:Then the original system equation becomes:
参见图5,混沌系统的Lyapunov指数谱可以看出,当控制信号的输入频率为ω=0.5,1.2,1.4,1.7,2.1,2.2,2.7~3,3.4~4.1,4.3,4.5~4.7,5.2,5.9,6.3,6.6.6.7,6.9,7.2,7.5~7.8,8,8.3,9.2和9.8~10时,此时系统的Lyapunov指数有两个大于0;此时本实施例产生的信号为超混沌信号。Referring to Figure 5, it can be seen from the Lyapunov exponent spectrum of the chaotic system that when the input frequency of the control signal is ω=0.5, 1.2, 1.4, 1.7, 2.1, 2.2, 2.7~3, 3.4~4.1, 4.3, 4.5~4.7, 5.2 , 5.9, 6.3, 6.6.6.7, 6.9, 7.2, 7.5~7.8, 8, 8.3, 9.2 and 9.8~10, at this time, two of the Lyapunov exponents of the system are greater than 0; chaotic signal.
实施例3Example 3
本实施例的能产生混沌信号的非线性电路,其系统方程为:The non-linear circuit that can produce chaotic signal of the present embodiment, its system equation is:
此系统的Lyapunov指数为:LE1=0.1827,LE2=0.0756,LE3=0.0756,LE4=-2.3920。The Lyapunov exponents of this system are: LE1=0.1827, LE2=0.0756, LE3=0.0756, LE4=-2.3920.
将正弦信号发生装置连接于该电路的第四个电路方程的非线形电路输入端,通过一乘法器接入非线性电路,正弦信号与信号输入x一起输入非线性电路输入端,构成一新的乘法项,该项的系数由输入信号的幅值和电位器共同决定。Connect the sinusoidal signal generating device to the input end of the nonlinear circuit of the fourth circuit equation of the circuit, connect the nonlinear circuit through a multiplier, and input the sinusoidal signal and the signal input x to the input end of the nonlinear circuit together to form a new The multiplication item, the coefficient of which is determined by the amplitude of the input signal and the potentiometer.
则原系统方程变为:Then the original system equation becomes:
参见图6,混沌系统的Lyapunov指数谱可以看出,当控制信号的输入频率为在ω=4.2~4.7和5.2~10时,此时系统的Lyapunov指数有两个大于0;此时本实施例产生的信号为超混沌信号。Referring to Fig. 6, it can be seen from the Lyapunov exponent spectrum of the chaotic system that when the input frequency of the control signal is at ω=4.2~4.7 and 5.2~10, two of the Lyapunov exponents of the system are greater than 0 at this moment; The generated signal is a hyperchaotic signal.
上述实施例中,能产生混沌信号的非线性电路的具体电路结构,通常由参数设置模块、积分模块、反馈模块、供电模块和输出模块构成;所述参数设置模块用于设置电路系统的参数;所述积分模块对参数设置模块输出电信号进行积分处理;所述反馈模块将积分模块输出的电信号反馈到参数设置模块的输入端;供电模块对参数设置模块和积分模块进行供电;所述输出模块作为系统的输出;本领域技术人员均可根据电路方程获知,在此不再赘述;正弦信号发生装置可选用RC振荡电路或现有的单片正弦信号发生芯片;正弦信号通过的输入频率及接入方式可通过运算或仿真获得。In the above embodiment, the specific circuit structure of the nonlinear circuit capable of generating chaotic signals is usually composed of a parameter setting module, an integral module, a feedback module, a power supply module and an output module; the parameter setting module is used to set the parameters of the circuit system; The integration module performs integral processing on the output electrical signal of the parameter setting module; the feedback module feeds back the electrical signal output by the integration module to the input terminal of the parameter setting module; the power supply module supplies power to the parameter setting module and the integration module; the output The module is used as the output of the system; those skilled in the art can know it according to the circuit equation, so I won’t repeat it here; the sinusoidal signal generator can choose RC oscillator circuit or existing single-chip sinusoidal signal generation chip; the input frequency and The access method can be obtained through calculation or simulation.
以上所述仅为本发明的优选实施例,并不用于限制本发明,显然,本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样,倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内,则本发明也意图包含这些改动和变型在内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.
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