Skip to main content
Log in

A chaotic synchronization system based on memristor for weak signal detection and its circuit implementation

Nonlinear Dynamics Aims and scope Submit manuscript

Cite this article


Traditional methods for detecting weak signals by using the critical thresholds and state transitions of chaotic systems have certain disadvantages, such as the complicated calculation of the critical thresholds and the difficulty of determining the states of operation of the system. To resolve these issues, the authors propose a van der Pol-Duffing chaotic synchronization system based on the memristor and examine its dynamic characteristics. The state of synchronization of the system is influenced when a signal is added to it, and the values of the parameters of the signal can be obtained by analyzing the errors in synchronization. The results of experiments showed that the proposed system needed less than 30 s to reach a stable synchronous state while maintaining a high efficiency of detection, where this is significantly shorter than the time taken by several widely used chaotic detection systems. Moreover, it could accurately detect the frequency, phase, and amplitude of the signal, and there was nearly no limit in its range of detection of the latter parameter. Furthermore, the authors implemented the proposed system in a circuit, and this verified the potential for implementing an accurate and efficient method of detecting multiple parameters of weak signals over a wide range of amplitudes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Data availability

The authors declare that the data supporting the findings of this study are available within the article.


  1. Li, Z., Su, H., Zhou, S., Hu, Q.: Signal fusion-based targets detection in the presence of clutter and subspace interference for multiple-input-multiple-output radar. IET Radar, Sonar Navigat. 13(1), 148–155 (2019)

    Article  Google Scholar 

  2. Xia, D.P., Zhang, Y., Cai, P., Huang, L.: An energy-efficient signal detection scheme for a radar-communication system based on the generalized approximate message-passing algorithm and low-precision quantization. IEEE Access 7, 29065–29075 (2019)

    Article  Google Scholar 

  3. Leite, V.C., da Silva, J.G.B., Veloso, G.F.C., da Silva, L.E.B., Lambert-Torres, G., Bonaldi, E.L., de Oliveira, L.E.D.L.: Detection of localized bearing faults in induction machines by spectral kurtosis and envelope analysis of stator current. IEEE Trans. Industr. Electron. 62(3), 1855–1865 (2014)

    Article  Google Scholar 

  4. Henao, H., Capolino, G.A., Fernandez-Cabanas, M., Filippetti, F., Bruzzese, C., Strangas, E., et al.: Trends in fault diagnosis for electrical machines: A review of diagnostic techniques. IEEE Ind. Electron. Mag. 8(2), 31–42 (2014)

    Article  Google Scholar 

  5. Li, W., Zhou, S., Willett, P., Zhang, Q.: Preamble detection for underwater acoustic communications based on sparse channel identification. IEEE J. Oceanic Eng. 44(1), 256–268 (2017)

    Article  Google Scholar 

  6. Siddagangaiah, S., Li, Y., Guo, X., Chen, X., Zhang, Q., Yang, K., Yang, Y.: A complexity-based approach for the detection of weak signals in ocean ambient noise. Entropy 18(3), 101 (2016)

    Article  Google Scholar 

  7. Yang, Z.C., Jiang, T., Xu, X.C., et al.: Research on correlation detection reference signal based on the reconstructed excitation signal for electromagnetic seismic vibrator. Chin. J. Geophys. 59(01), 318–329 (2016)

    Google Scholar 

  8. Zheng, Y., Chen, X., Zhu, R.: Frequency hopping signal detection based on wavelet decomposition and Hilbert-Huang transform. Mod. Phys. Lett. B 31(19–21), 1740078 (2017)

    Article  MathSciNet  Google Scholar 

  9. Palahina, E., Gamcov\(\acute{a}\), M., Gladi\({\check{s}}\)ov\(\acute{a}\), I., Gamec, J., Palahin, V. Signal detection in correlated non-gaussian noise using higher-order statistics. Circuits, Systems, and Signal Processing, 37, 1704–1723 (2018)

  10. Qiao, Z.C., Tang, L.X., Liu, H.: Adaptive filtering algorithm for cancelling the pump noise in the mud pulse signal. Chinese J. Scient. Instr. 37(07), 1477–1484 (2016)

    Google Scholar 

  11. Li, Y., Yang, B.: Chaotic system for the detection of periodic signals under the background of strong noise. Chin. Sci. Bull. 48, 508–510 (2003)

    Article  Google Scholar 

  12. Liu, H.G., Liu, X.L., Yang, J.H., Sanjun, M.A., Cheng, G.: Detecting the weak high-frequency character signal by vibrational resonance in the Duffing oscillator. Nonlinear Dyn. 89, 2621–2628 (2017)

    Article  MathSciNet  Google Scholar 

  13. Sen, B., Wang, J.: Stator interturn fault detection in permanent-magnet machines using PWM ripple current measurement. IEEE Trans. Industr. Electron. 63(5), 3148–3157 (2016)

    Article  Google Scholar 

  14. Wang, G., Chen, D., Lin, J., Chen, X.: The application of chaotic oscillators to weak signal detection. IEEE Trans. Industr. Electron. 46(2), 440–444 (1999)

    Article  Google Scholar 

  15. Zhihong, Z., Yang, S.: Application of van der Pol-Duffing oscillator in weak signal detection. Comput. Electr. Eng. 4, 1–8 (2015)

    Article  Google Scholar 

  16. Gokyildirim, A., Uyaroglu, Y., Pehlivan, I.: A weak signal detection application based on hyperchaotic Lorenz system. Tehni\({\check{c}}\)ki vjesnik 25(3), 701–708 (2018)

  17. Li, G., Cui, J., Yang, H.: A new detecting method for underwater acoustic weak signal based on differential double coupling oscillator. IEEE Access 9, 18842–18854 (2021)

    Article  Google Scholar 

  18. Wang, K., Yan, X., Yang, Q., Hao, X., Wang, J.: Weak signal detection based on strongly coupled Duffing-Van der Pol oscillator and long short-term memory. J. Phys. Soc. Jpn. 89(1), 014003 (2020)

  19. Xie, F., Zhang, B., Yang, R., Iu, H.H.C.: Detecting bifurcation types and characterizing stability in DC\(-\)DC switching converters by duplicate symbolic sequence and weight complexity. IEEE Trans. Industr. Electron. 60(8), 3145–3156 (2012)

    Article  Google Scholar 

  20. Zhang, T., Feng, G.: Output tracking of piecewise-linear systems via error feedback regulator with application to synchronization of nonlinear Chua’s circuit. IEEE Trans. Circuits Syst. I Regul. Pap. 54(8), 1852–1863 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, G., Zhang, B.: A novel weak signal detection method via chaotic synchronization using Chua’s circuit. IEEE Trans. Industr. Electron. 64(3), 2255–2265 (2016)

    Article  Google Scholar 

  22. Li, G., Tan, N.L., Su, S.Q., Zhang, C.: Unknown frequency weak signal detection based on Lorenz chaotic synchronization system. J. Vibr. Shock 38(5), 155–161 (2019)

    Google Scholar 

  23. Yang, J.J., Strukov, D.B., Stewart, D.R.D.: Memristive devices for computing. Nat. Nanotechnol. 8, 13–24 (2012)

    Article  Google Scholar 

  24. Min, F., Luo, A.C.: On parameter characteristics of chaotic synchronization in two nonlinear gyroscope systems. Nonlinear Dyn. 69, 1203–1223 (2012)

    Article  MathSciNet  Google Scholar 

  25. Peng, G., Min, F.: Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit. Nonlinear Dyn. 90(3), 1607–1625 (2017)

    Article  Google Scholar 

  26. Brezetskyi, S., Dudkowski, D., Kapitaniak, T.: Rare and hidden attractors in Van der Pol-Duffing oscillators. Eur. Phys. J. Special Topics 224(8), 1459–1467 (2015)

    Article  Google Scholar 

  27. Bao, B.C., Xu, J.P., Zhou, G.H., Ma, Z.H., Zou, L.: Chaotic memristive circuit: equivalent circuit realization and dynamical analysis. Chin. Phys. B 20(12), 120502 (2011)

    Article  Google Scholar 

  28. Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifur. Chaos 20(05), 1567–1580 (2010)

    Article  Google Scholar 

  29. Yu, D.S., Liang, Y., Chen, H., Iu, H.H.: Design of a practical memcapacitor emulator without grounded restriction. IEEE Trans. Circuits Syst. II Express Briefs 60(4), 207–211 (2013)

    Google Scholar 

  30. Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80–83 (2008)

    Article  Google Scholar 

  31. Hu, F.W., Bao, B.C., Wu, H.G., Wang, C.L.: Equivalent circuit analysis model of charge-controlled memristor and its circuit characteristics. Acta Physica Sinica 62(21), 404–411 (2013)

    Google Scholar 

  32. Dong, K., Xu, K., Zhou, Y., Zuo, C., Wang, L., Zhang, C., et al.: A memristor-based chaotic oscillator for weak signal detection and its circuitry realization. Nonlinear Dyn. 109(3), 2129–2141 (2022)

    Article  Google Scholar 

  33. Liu, Y., Zhang, X.C.: A new method based on Lyapunov exponent to determine the threshold of chaotic systems. Appl. Mech. Mater. 511–512, 329–333 (2014)

    Google Scholar 

  34. Hu, W.J., Liu, Z.Z., Li, Z.H.: Quantitative analysis of noise impact on duffing chaotic detection system using Lyapunov characteristic exponents. Appl. Mech. Mater. 130–134, 1331–1337 (2011)

    Article  Google Scholar 

  35. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821 (1990)

  36. Li, G., Zhang, B.: A novel method for detecting weak signal with unknown frequency based on Duffing oscillator. Chinese J. Scient. Instr. 38(1), 181–189 (2017)

    Google Scholar 

  37. Vincent, U.E., Odunaike, R.K., Laoye, J.A., Gbindinninuola, A.A.: Adaptive backstepping control and synchronization of a modified and chaotic Van der Pol-Duffing oscillator. J. Contr. Theory Appl. 9(2), 273–277 (2011)

Download references


This study was funded by the National Natural Science Foundation of China [Grant Nos. 51501168, 41574175, 41204083], the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) [Grant Nos. CUG150632 and CUGL160414].

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Kaifeng Dong, Fang Jin or Junlei Song.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, K., Xu, K., Wang, L. et al. A chaotic synchronization system based on memristor for weak signal detection and its circuit implementation. Nonlinear Dyn 111, 22013–22032 (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: