Weak periodic signal detection method and system based on improved Genesio-Tesi chaotic system

Abstract

The present invention relates to a weak periodic signal detection method and system based on an improved Genesio-Tesi chaotic system. The detection model of the detection system is: wherein x, y, z are state variables of the system, a, b, c, d, e, f are model parameters; k is a built-in driving force; w is a frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the frequency of the signal to be measured; h(t) is an input signal under different noise backgrounds, h(t)=n(t)+s(t), n(t) is a noise signal, s(t ) is the weak periodic signal to be detected; d≠0, a, b, c, e, f must satisfy the following relationship: a>0, bf>0, cef[1+ksin(wt)]>0abf‑cef‑cefksin(wt)>0; by adjusting the built-in driving force k of the detection model to make it in the critical state of transition from chaotic state to periodic state at the initial stage of detection, the chaotic weak periodic signal detection is carried out in the region where the improved Genesio‑Tesi system transitions from chaotic state to periodic state; the detection system can realize weak periodic signal detection with good detection effect.

Description

Technical Field

[0001] The present invention relates to the technical field of signal detection, and in particular to a weak periodic signal detection method and system based on an improved Genesio-Tesi chaotic system. Background Art

[0002] Compared with traditional weak signal detection, the advantages of chaotic weak signal detection are strong anti-noise ability and sensitivity to small disturbances. It has been applied to underwater acoustic detection, fault detection, acoustic wave communication and other fields. As one of the hot spots in the field of chaos application, weak signal detection is often performed by scholars at home and abroad using Duffing oscillators. However, the weak signal detection of the Duffing system has reached a bottleneck, so scholars have begun to start from other systems to find breakthroughs and improve detection performance.

[0003] In 2012, Wang Mengjiao and others realized non-feedback chaotic control of the Chen system with non-resonant parameter excitation, and on this basis, used the controlled Chen system for chaotic weak signal detection. In 2014, Zhou Fang and others used dual-parameter perturbation to complete the weak signal detection and circuit implementation of the Lorentz-like system. In 2018, Liu Jianming and others embedded the cosine function into the Liu system to form a Liu-cos system, performed weak signal detection based on the Liu-cos system, and used intermittent chaos to detect unknown signals containing noise. In 2020, Li proposed a new method for bearing fault diagnosis that combines coupled Lorentz systems with power spectrum technology. In 2021, Wang Weihao and others embedded the cosine function as an internal excitation source into the LV system and obtained a chaotic weak signal detection system with a detectable signal-to-noise ratio as low as -66dB.

[0004] In 1992, Genesio and Tesi proposed the Genesio-Tesi system based on the principle of harmonic balance. Currently, the Genesio-Tesi system is mostly used in the fields of chaotic synchronization and chaotic secure communication. At present, the research on the detection of chaotic weak periodic signals of the Genesio-Tesi system is still in a blank stage. Summary of the invention

[0005] The purpose of the present invention is to provide a weak periodic signal detection method based on an improved Genesio-Tesi chaotic system. The method performs chaotic weak periodic signal detection through an improved Genesio-Tesi equation, and the method has a minimum signal-to-noise ratio of -46dB under a continuous white noise background; it also has a good detection effect under different color noise backgrounds, among which the detection effect is best under a purple noise background, and the minimum detectable signal-to-noise ratio reaches -52dB.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] A weak periodic signal detection method based on an improved Genesio-Tesi chaotic system, the method comprising the following steps:

[0008] Step S1, constructing an improved Genesio-Tesi chaotic system. The detection model of the improved Genesio-Tesi chaotic system is:

[0009]

[0010] In the formula, x, y, z are the state variables of the system, a, b, c, d, e, f are all model parameters; k is the built-in driving force; w is the frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the signal frequency to be measured; h(t) is the input signal under different noise backgrounds, h(t) = n(t) + s(t), n(t) is the noise signal, s(t) is the weak periodic signal to be measured; d≠0, a, b, c, e, f must satisfy the following relationship:

[0011] a>0,bf>0,cef[1+ksin(wt)]>0

[0012] abf-cef-cefksin(wt)>0;

[0013] Step S2, setting the parameters and initial values ​​of the detection model in the system, adjusting the built-in driving force k, so that the improved Genesio-Tesi chaotic system is in a critical state of transition from a chaotic state to a periodic state;

[0014] Step S3: Import the input signal h(t) under different noise backgrounds into the system, and let the built-in driving force be k d , and then add the weak sinusoidal signal to be detected at the same frequency As a periodic disturbance, the amplitude of the weak sinusoidal signal is r, and the total driving force in the improved Genesio-Tesi chaotic system becomes:

[0015]

[0016] θ is the phase of the signal to be measured

[0017] k′=(k d 2 +2k d rcosθ+r 2 ) 1 / 2

[0018] k' can be approximately equivalent to k d +r, after adding r, k' becomes larger, and the system changes from an unstable chaotic state to a quasi-periodic state;

[0019]

[0020] When k d >>r, then The impact of can be ignored;

[0021] Step S4, using the region where the improved Genesio-Tesi system changes from a chaotic state to a periodic state to detect a chaotic weak periodic signal; if the system phase diagram and time series show a periodic state or a quasi-periodic state, it means that there is a detection signal; if the system is still in a chaotic state after the signal is input, it means that there is no signal to be tested.

[0022] As a preferred embodiment of the present invention, the parameters of step S2 are set as a=0.62, b=1, c=1, d=1, e=1, f=1, w=1 or 2 or 5, and the built-in driving force k=0.4117.

[0023] As a preferred embodiment of the present invention, when calculating the amplitude of the weak sinusoidal signal, it is calculated based on the difference between the total driving force and the built-in driving force.

[0024] Another object of the present invention is to provide a weak periodic signal detection system based on an improved Genesio-Tesi chaotic system, which can realize weak periodic signal detection, and the minimum signal-to-noise ratio under a continuous white noise background reaches -46dB; it also has good detection effects under different color noise backgrounds, among which the detection effect is best under the background of purple noise, and the minimum detectable signal-to-noise ratio reaches -52dB.

[0025] A weak periodic signal detection system based on an improved Genesio-Tesi chaotic system. The detection model of the detection system is:

[0026]

[0027] In the formula, x, y, z are the state variables of the system, a, b, c, d, e, f are all model parameters; k is the built-in driving force; w is the frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the signal frequency to be measured; h(t) is the input signal under different noise backgrounds, h(t) = n(t) + s(t), n(t) is the noise signal, s(t) is the weak periodic signal to be measured; d≠0, a, b, c, e, f must satisfy the following relationship:

[0028] a>0,bf>0,cef[1+ksin(wt)]>0

[0029] abf-cef-cefksin(wt)>0;

[0030] The improved Genesio-Tesi chaotic system adjusts the built-in driving force k of the detection model to make it in a critical state of transition from a chaotic state to a periodic state at the initial stage of detection. The chaotic weak periodic signal detection is carried out in the transition area from the chaotic state to the periodic state of the improved Genesio-Tesi system. If the input signal under different noise backgrounds is introduced into the system, the system phase diagram and time series show a periodic state or a quasi-periodic state, then there is a detection signal; if the system is still in a chaotic state after the signal is input, then there is no signal to be tested.

[0031] As a preferred embodiment of the present invention, wherein a=0.62, b=1, c=1, d=1, e=1, f=1, w=1 or 2 or 5, the built-in driving force k=0.4117.

[0032] As a preferred embodiment of the present invention, the signal detected by the improved Genesio-Tesi chaotic system is a sinusoidal signal with substantially the same frequency as the model.

[0033] Advantages and beneficial effects of the present invention: The present invention uses the improved Genesio-Tesi equation for the first time to detect chaotic weak periodic signals. The detection method is suitable for detecting weak periodic signals under a continuous white noise background, and the minimum detectable signal-to-noise ratio of the signal reaches -46dB; it also has good detection effects under different color noise backgrounds, among which the detection effect is best under the background of purple noise, and the minimum detectable signal-to-noise ratio reaches -52dB. The system uses chaotic weak signal detection, which has the advantages of strong noise resistance and sensitivity to small disturbances compared to traditional weak signal detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Time series, phase diagram, Poincare cross section and Lyapunov index spectrum of the improved Genesio-Tesi chaotic system: (a) time series with initial value (0.1, 0.101, 0.1), (b) time series with initial value (0.1, 0.102, 0.1), (c) xy phase diagram, (d) xz phase diagram, (e) yz phase diagram, (f) xyz phase diagram, (g) Poincare cross section, (h) Lyapunov index spectrum, (i) power spectrum.

[0035] Figure 2 This is the graph of Lyapunov index changing with k.

[0036] Figure 3 It is the Simulink model of the improved Genesio-Tesi chaotic weak periodic signal detection system.

[0037] Figure 4Figure 3: The xy phase diagram and time series of the improved Genesio-Tesi chaotic weak periodic signal detection system: (a) xy phase diagram when there is no small signal and noise input, (b) time series when there is no small signal and noise input, (c) xy phase diagram when noise is input but not small signal, (d) time series when noise is input but not small signal, (e) xy phase diagram when small signal is input but not noise, (f) time series when small signal is input but not noise, (g) xy phase diagram when small signal is input under noise background, (h) time series when small signal is input under noise background. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0039] Example 1

[0040] A weak periodic signal detection method based on an improved Genesio-Tesi chaotic system, the method comprising the following steps:

[0041] Step S1, constructing an improved Genesio-Tesi chaotic system. The detection model of the improved Genesio-Tesi chaotic system is:

[0042]

[0043] In the formula, x, y, z are the state variables of the system, a, b, c, d, e, f are all model parameters; k is the built-in driving force; w is the frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the signal frequency to be measured; h(t) is the input signal under different noise backgrounds, h(t) = n(t) + s(t), n(t) is the noise signal, s(t) is the weak periodic signal to be measured; d≠0, a, b, c, e, f must satisfy the following relationship:

[0044] a>0,bf>0,cef[1+ksin(wt)]>0

[0045] abf-cef-cefksin(wt)>0;

[0046] Step S2, setting the parameters and initial values ​​of the detection model in the system, adjusting the built-in driving force k, so that the improved Genesio-Tesi chaotic system is in a critical state of transition from a chaotic state to a periodic state;

[0047] Step S3: Import the input signal h(t) under different noise backgrounds into the system, and let the built-in driving force be k d , and then add the weak sinusoidal signal to be detected at the same frequency As a periodic disturbance, the amplitude of the weak sinusoidal signal is r, and the total driving force in the improved Genesio-Tesi chaotic system becomes:

[0048]

[0049] θ is the phase of the signal to be measured

[0050] k′=(k d 2 +2k d rcosθ+r 2 ) 1 / 2

[0051] k' can be approximately equivalent to k d +r, after adding r, k' becomes larger, and the system changes from an unstable chaotic state to a quasi-periodic state;

[0052]

[0053] When k d >>r, then The impact of can be ignored;

[0054] Step S4, using the region where the improved Genesio-Tesi system changes from a chaotic state to a periodic state to detect a chaotic weak periodic signal; if the system phase diagram and time series show a periodic state or a quasi-periodic state, it means that there is a detection signal; if the system is still in a chaotic state after the signal is input, it means that there is no signal to be tested.

[0055] When calculating the amplitude of the weak sinusoidal signal, the present invention can calculate it according to the difference between the total driving force and the built-in driving force.

[0056] The key of the present invention is to use the improved Genesio-Tesi chaotic system to detect weak sound wave signals. In order to enable those skilled in the art to clearly understand the technical solution of the present invention, the improved Genesio-Tesi chaotic system is introduced in detail below.

[0057] In order to detect weak sound wave signals, the chaotic system needs to contain periodic functions. The present invention improves the Genesio-Tesi equation by adding a perturbation term, so that the improved Genesio-Tesi equation is:

[0058]

[0059] Where a, b, c, d, e, and f are all system parameters, k is the driving force, and w is the frequency.

[0060] In order to realize the detection of weak signals by using the improved Genesio-Tesi equation, the present invention needs to ensure the stability of its dynamics, and also needs to set the system parameters so that the improved Genesio-Tesi system has chaotic characteristics.

[0061] (1) Dissipation

[0062]

[0063] When a>0, the time-averaged divergence ΔV of the improved Genesio-Tesi system is <0, the system is a dissipative system, the volume in the phase space shrinks at an exponential rate, and it has a stable attractor.

[0064] (2) Balance point analysis

[0065] Using the right side of equation (1) equal to zero, we get

[0066]

[0067] In the first equation of equation group (1), the system parameter e≠0, ksin(wt) is the perturbation term, 1+ksin(wt)≠0, and the equilibrium point is E 1 (c / d, 0, 0) and E 2 (0, 0, 0), two in total.

[0068] Balance Point E 1 The Jacobi matrix J(E 1 )for

[0069]

[0070] |J-λ I|=0 (5)

[0071]

[0072] Its characteristic equation is

[0073] λ 3 +aλ 2 +bfλ+cef[1+ksin(wt)]=0 (7)

[0074] According to the Routh-Hurwitz theorem,

[0075] a>0,bf>0,cef[1+ksin(wt)]>0 (8)

[0076]

[0077] abf-cef-cefksin(wt)>0 (10)

[0078] When the system parameter f≠0, the product of the system parameters b and f is greater than 0. When f>0, we can get from equations (8) and (10):

[0079]

[0080] If the product of system parameters c and e is greater than 0, then

[0081] k sin(wt)+1>0 (12)

[0082] w≠0, we get

[0083] -1<k<1 (13)

[0084] If the product of system parameters c and e is less than 0, then

[0085] k sin(wt)+1<0 (14)

[0086] When sin(wt)=0, the above formula is meaningless, because t≥0, there exists wt=kπ, which satisfies sin(wt)=0, so it is not appropriate.

[0087] When the system parameter f<0, we can get

[0088]

[0089] If the product of system parameters c and e in (4) is greater than 0, then

[0090] k sin(wt)+1<0 (16)

[0091] Similarly, there exists wt=kπ, satisfying sin(wt)=0, which is also inappropriate.

[0092] If the product of system parameters c and e is less than 0, then

[0093] k sin(wt)+1>0 (17)

[0094] -1<k<1 (18)

[0095] After sorting out the above situations, we can get the equilibrium point E in Table 1 1 Analyze the situation.

[0096] Table 1 Balance point E 1 Analyze the situation

[0097]

[0098] Similarly, for the equilibrium point E2 After analysis, we can get the equilibrium point E 2 Analyze the situation.

[0099] The present invention determines the value range of K, k∈(-1, 1) through equilibrium point analysis; in addition, the present invention determines that when the system parameters a=0.62, b=1, c=1, d=1, e=1, f=1, w=1 or 2 or 5, the improved Genesio-Tesi system has chaotic characteristics and has a good detection effect by repeatedly testing and studying and analyzing the changes of the Lyapunov exponent with the system parameters.

[0100] (3) Chaotic characteristics of the improved Genesio-Tesi system

[0101] The present invention uses Matlab to solve the improved Genesio-Tesi system using the fourth-order Runge-Kutta method, sets the system parameters a=0.62, b=1, c=1, d=1, e=1, f=1, k=0.38, w=1, and uses the numerical results to draw the time series, phase diagram, Poincare cross section, and Lyapunov index spectrum of the improved Genesio-Tesi system, as shown in FIG. Figure 1 shown.

[0102] Depend on Figure 1 (a) and Figure 1 (b) It can be seen that although the initial values ​​of the modified Genesio-Tesi system are very different, the long-term evolution behavior is also different, which reflects the sensitivity of the chaotic system to the initial value. The time series is random and disordered, which proves that the system is in a chaotic state. Figure 1 (c) Figure 1 (d) Figure 1 (e) Figure 1 (f) is the phase diagram of the chaotic state of the improved Genesio-Tesi system. It can be seen that each phase plane trajectory is a chaotic attractor, which is ergodic, bounded, and random. Figure 1 (g) There are dense points scattered in patches on the Poincare cross section of the improved Genesio-Tesi system, indicating that the system is in a chaotic state. Figure 1 (h) Lyapunov Exponents (LE) indicate how fast two adjacent orbits in phase space separate over time. LE1 is the Lyapunov exponent corresponding to variable x. It can be seen that LE1 is near 0 during the period of 0-500, which indicates a transient stage. After that, LE1>0; Lyapunov exponent>0, which proves that the system is in a chaotic state. Figure 1(I) is the power spectrum of the improved Genesio-Tesi system, where the continuous spectrum indicates that the system is in a chaotic state, and the peak represents the frequency of the random orbit with the highest probability of appearing in the chaotic attractor.

[0103] (4) Detection of chaotic weak periodic signals in the improved Genesio-Tesi system

[0104] In order to realize the detection of chaotic weak signals, the present invention first needs to find the critical region of chaos and period through Lyapunov index. Set the system parameters to a = 0.62, b = 1, c = 1, d = 1, e = 1, f = 1, w = 1, when k ∈ [0, 0.8000], the Lyapunov index changes with k as follows Figure 2 shown.

[0105] like Figure 2 As shown in the figure, the improved Genesio-Tesi system has a chaotic and periodic critical region, and LE1 shows how the dynamic behavior of the variable x changes with k. At the beginning, the driving force is low, LE1<0, and the system is in a periodic state. At this time, the influence of the driving force on the system is equivalent to the influence of the system parameter e on the system, that is, the system can be put into a chaotic state by increasing the parameter e or increasing the driving force. As the driving force increases further, the chaos of the system weakens, the periodicity becomes more prominent, and the system returns from the chaotic state to the periodic state. Figure 2 It can be seen that when k>0.42, LE1<0, which indicates that when the system is in a periodic state near k=0.42, the region of transition from chaotic state to periodic state can be used to detect chaotic weak periodic signals, and the threshold region is between 0.4117-0.4118.

[0106] The present invention adds h(t)=n(t)+s(t) at the driving force, where h(t) is the input signal under different noise backgrounds, n(t) is the noise signal, and s(t) is the weak periodic signal to be measured. Then the detection model of the improved Genesio-Tesi chaotic system is:

[0107]

[0108] Assume that the system is in a critical state of transition from chaotic state to periodic state, and let the built-in driving force be k d , and then add the weak sinusoidal signal to be detected at the same frequency As a periodic disturbance, the small signal amplitude is r, and the total driving force in the improved Genesio-Tesi system becomes

[0109]

[0110] θ is the phase of the signal to be measured

[0111] k′=(kd 2 +2k d rcosθ+r 2 ) 1 / 2 (twenty one)

[0112] k' can be approximately equivalent to k d +r, after adding r, k' becomes larger, and the system changes from an unstable chaotic state to a quasi-periodic state.

[0113]

[0114] When k d >>r, then The impact can be ignored.

[0115] The present invention utilizes the characteristics of the chaotic system that it has strong anti-noise ability and is sensitive to small disturbances, and determines the other system parameters and initial values ​​of the improved Genesio-Tesi chaotic weak periodic signal detection system in addition to the driving force k, and adjusts k=k d , let the initial state of the system be in an unstable chaotic state, and import the noise h(t) under different noise backgrounds into the system. If the system phase diagram and time series show a periodic state or a quasi-periodic state, it means that there is a detection signal; if the system is still in a chaotic state after the signal is input, it means that there is no signal to be measured.

[0116] (5) Research on the improved Genesio-Tesi chaotic weak periodic signal detection system under different noise backgrounds

[0117] Build as Figure 3 The improved Genesio-Tesi chaotic weak periodic signal detection system Simulink model shown in the figure sets the system parameters to a=0.62, b=1, c=1, d=1, e=1, f=1, w=1, and k=0.4117. It can output xy phase diagram, xz phase diagram, yz phase diagram, and time series about x. It can also transfer the noise, x, y, and z values ​​to Matlab Workspace and perform data processing through Matlab.

[0118] When the input signal h(t) = 0, after the system is disturbed by the periodic driving force, the phase diagram and time series are as follows Figure 4 (a) and Figure 4 (b) shows the critical chaotic state. From the time series, we can see that after a period of iteration, the system Figure 1 For (a), the periodicity is obvious, but the chaos is still retained. Using the Band-Limited WhiteNoise module in Simulink, a Gaussian white noise with a power of 0.0005w is added. Figure 4As shown in (d), the time series has burrs due to noise. This shows that the system has strong anti-noise ability. In the absence of noise, a small periodic signal with an amplitude of r = 0.001 is added, as shown in Figure 4 (e) and Figure 4 As shown in (f), the phase diagram trajectory of the system converges from the chaotic state to the limit cycle, and the boundary value shrinks. The time series is neat and flat. Figure 4 (g) and Figure 4 After adding Gaussian white noise with a power of 0.0005W and a periodic small signal with an amplitude of r=0.001 to the system shown in (h), the phase diagram becomes rough and band-shaped on the ring due to the noise, and burrs appear on the time series noise.

[0119] If there is only signal but no noise, any weak signal can be detected after arbitrary amplification in theory. Therefore, the detection capability of the system actually depends on the signal-to-noise ratio (SNR). As an important indicator of the detection capability of the detection system, the signal-to-noise ratio is usually not measured directly, but calculated by measuring the amplitude of the noise signal.

[0120]

[0121] at this time, Figure 3 The lowest detectable SNR of the system under the selected system parameters is -46.9897dB.

[0122] Noise is not only white noise, but also colored noise. Compared with white noise, the power spectrum of colored noise is not flat. The shape of the power spectrum density function determines the "color" of the noise, which is similar to the spectral distribution. Common noises include blue noise, pink noise, purple noise, etc. Colored noise can be generated with the help of Simulink's Colored Noise module.

[0123] The simulation results show that the improved Genesio-Tesi chaotic weak periodic signal detection system can also achieve good detection results under blue noise, pink noise and purple noise. The minimum detectable SNR of purple noise exceeds the minimum detectable SNR of white noise, reaching -52.2557dB. The SNR under various color noise backgrounds is shown in Table 3.

[0124] Table 3 SNR of various types of color noise

[0125]

[0126] in conclusion:

[0127] The present invention improves the Genesio-Tesi equation, and finds the driving force value range by performing dynamic stability analysis on it. The critical region of chaos and period is found by Lyapunov exponent. Through Simulink simulation, the state change of the improved Genesio-Tesi system is comprehensively judged by using phase diagram and time series, and weak periodic signal detection is performed. The minimum signal-to-noise ratio under the background of continuous white noise reaches -46dB. There is also a good detection effect under different color noise backgrounds, among which the detection effect is best under the background of purple noise, and the minimum detectable signal-to-noise ratio reaches -52dB.

Claims

1. A weak periodic signal detection method based on improved Genesio-Tesi chaotic system, It is characterized in that The method comprises the following steps: Step S1, constructing an improved Genesio-Tesi chaotic system. The detection model of the improved Genesio-Tesi chaotic system is: In the formula, x, y, z are the state variables of the system, a, b, c, d, e, f are all model parameters; k is the built-in driving force; w is the frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the signal frequency to be measured; h(t) is the input signal under different noise backgrounds, h(t) = n(t) + s(t), n(t) is the noise signal, s(t) is the weak periodic signal to be measured; d≠0, a, b, c, e, f must satisfy the following relationship: a>0,bf>0,cef[1+ksin(wt)]>0 abf-cef-cefk sin(wt)>0; Step S2, setting the parameters and initial values ​​of the detection model in the system, adjusting the built-in driving force k, so that the improved Genesio-Tesi chaotic system is in a critical state of transition from a chaotic state to a periodic state; Step S3: Import the input signal h(t) under different noise backgrounds into the system, and let the built-in driving force be k d , and then add the weak sinusoidal signal to be detected at the same frequency As a periodic disturbance, the amplitude of the weak sinusoidal signal is r, and the total driving force in the improved Genesio-Tesi chaotic system becomes: θ is the phase of the signal to be measured k′=(k d 2 +2k d r cosθ+r 2 ) 1 / 2 k' can be approximately equivalent to k d +r, after adding r, k' becomes larger, and the system changes from an unstable chaotic state to a quasi-periodic state; When k d >>r, then The impact of can be ignored; Step S4, using the region where the improved Genesio-Tesi system changes from a chaotic state to a periodic state to detect a chaotic weak periodic signal; if the system phase diagram and time series show a periodic state or a quasi-periodic state, it means that there is a detection signal; if the system is still in a chaotic state after the signal is input, it means that there is no signal to be tested.

2. According to claim 1, a weak periodic signal detection method based on an improved Genesio-Tesi chaotic system, It is characterized in that The parameters of step S2 are set as a=0.62, b=1, c=1, d=1, e=1, f=1, w=1 or 2 or 5, and the built-in driving force k=0.4117.

3. A weak periodic signal detection method based on an improved Genesio-Tesi chaotic system according to claim 1 or 2, It is characterized in that When calculating the amplitude of a weak sinusoidal signal, it is calculated based on the difference between the total driving force and the built-in driving force.

4. A weak periodic signal detection system based on an improved Genesio-Tesi chaotic system. It is characterized in that The detection model of the detection system is: In the formula, x, y, z are the state variables of the system, a, b, c, d, e, f are all model parameters; k is the built-in driving force; w is the frequency, and the w value of the detection model is determined by scaling according to the signal to be measured to ensure that the model frequency is basically consistent with the signal frequency to be measured; h(t) is the input signal under different noise backgrounds, h(t) = n(t) + s(t), n(t) is the noise signal, s(t) is the weak periodic signal to be measured; d≠0, a, b, c, e, f must satisfy the following relationship: a>0,bf>0,cef[1+ksin(wt)]>0 abf-cef-cefk sin(wt)>0; The improved Genesio-Tesi chaotic system adjusts the built-in driving force k of the detection model to make it in a critical state of transition from a chaotic state to a periodic state at the initial stage of detection. The chaotic weak periodic signal detection is carried out in the transition area from the chaotic state to the periodic state of the improved Genesio-Tesi system. If the input signal under different noise backgrounds is introduced into the system, the system phase diagram and time series show a periodic state or a quasi-periodic state, then there is a detection signal; if the system is still in a chaotic state after the signal is input, then there is no signal to be tested.

5. A weak periodic signal detection system based on an improved Genesio-Tesi chaotic system according to claim 4, It is characterized in that Wherein a=0.62,b=1,c=1,d=1,e=1,f=1,w=1 or 2 or 5,and the built-in driving force k=0.4117.

6. A weak periodic signal detection system based on an improved Genesio-Tesi chaotic system according to claim 4 or 5, It is characterized in that The signal detected by the improved Genesio-Tesi chaotic system is a sinusoidal signal with basically the same frequency as the model.

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