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Implementation of a memristor-based 4D chaotic oscillator and its nonlinear control

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Abstract

In this study, an electronic model of a memristive-based 4D autonomous chaotic system with a line equilibrium is proposed. A memristor offers many advantages because of its superior properties for improving different circuits, e.g., chaotic circuits and systems. In particular, its nonlinearity and nonvolatile behavior provide a unique opportunity to design chaotic circuits. Therefore, we designed a flux-controlled memristor-based 4D autonomous chaotic system having a line equilibrium. The fundamental dynamical properties of the system are demonstrated with regards to equilibrium, Jacobian matrices, Lyapunov exponents, and bifurcation behavior. A nonlinear controller based on the Lyapunov stability method was also designed to control the novel system. Furthermore, it is controlled by only one state controller. As was expected, both theoretical and simulation results of the 4D chaotic oscillator were in good agreement with the experimental results.

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References

  1. Chua, L. (1971). Memristor-The missing circuit element. IEEE Transactions on Circuit Theory, 18(5), 507–519.

    Google Scholar 

  2. Chua, L. O., & Kang, S. M. (1976). Memristive devices and systems. Proceedings of the IEEE, 64(2), 209–223.

    MathSciNet  Google Scholar 

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

    Google Scholar 

  4. Sanchez-Lopez, C., Mendoza-Lopez, J., Carrasco-Aguilar, M. A., & Muniz-Montero, C. (2014). A floating analog memristor emulator circuit. IEEE Transactions on Circuits and Systems II: Express Briefs, 61(5), 309–313.

    Google Scholar 

  5. Ranjan, R. K., Rani, N., Pal, R., Paul, S. K., & Kanyal, G. (2017). Single CCTA based high frequency floating and grounded type of incremental/decremental memristor emulator and its application. Microelectronics Journal, 60, 119–128.

    Google Scholar 

  6. Yu, D., Iu, H. H. C., Fitch, A. L., & Liang, Y. (2014). A floating Memristor emulator based relaxation oscillator. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(10), 2888–2896.

    Google Scholar 

  7. Yesil, A., Babacan, Y., & Kacar, F. (2019). Design and experimental evolution of memristor with only one VDTA and one capacitor. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 38(6), 1123–1132.

    Google Scholar 

  8. Abuelma’atti, M. T., & Khalifa, Z. J. (2016). A new floating memristor emulator and its application in frequency-to-voltage conversion. Analog Integrated Circuits and Signal Processing, 86(1), 141–147.

    Google Scholar 

  9. Yesil, A., Babacan, Y., & Kacar, F. (2014). A new DDCC based memristor emulator circuit and its applications. Microelectronics Journal, 45(3), 282–287.

    Google Scholar 

  10. Bao, H., Zhang, Y., Liu, W., & Bao, B. (2020). Memristor synapse-coupled memristive neuron network: Synchronization transition and occurrence of chimera. Nonlinear Dynamics, 100(1), 937–950.

    MATH  Google Scholar 

  11. Babacan, Y., Kaçar, F., & Gürkan, K. (2016). A spiking and bursting neuron circuit based on memristor. Neurocomputing, 203, 86–91.

    Google Scholar 

  12. Muthuswamy, B., & Chua, L. O. (2010). Simplest chaotic circuit. International Journal of Bifurcation and Chaos, 20(5), 1567–1580.

    Google Scholar 

  13. Sahin, M. E., Demirkol, A. S., Guler, H., & Hamamci, S. E. (2020). Design of a hyperchaotic memristive circuit based on wien bridge oscillator. Computers and Electrical Engineering, 88, 106826.

    Google Scholar 

  14. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the atmospheric sciences, 20(2), 130–141.

    MathSciNet  MATH  Google Scholar 

  15. Rössler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397–398.

    MATH  Google Scholar 

  16. Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821–824.

    MathSciNet  MATH  Google Scholar 

  17. Sprott, J. C. (1994). Some simple chaotic flows. Physical Review E, 50(2), R647–R650.

    MathSciNet  Google Scholar 

  18. Sprott, J. C. (1997). Simplest dissipative chaotic flow. Physics Letters, Section A: General, Atomic and Solid State Physics, 228(4–5), 271–274.

    MathSciNet  MATH  Google Scholar 

  19. Chen, G., & Ueta, T. (1999). Yet another chaotic attractor. International Journal of Bifurcation and Chaos, 09(07), 1465–1466.

    MathSciNet  MATH  Google Scholar 

  20. Lü, J., & Chen, G. (2002). A new chaotic attractor coined. International Journal of Bifurcation and Chaos, 12(03), 659–661.

    MathSciNet  MATH  Google Scholar 

  21. Feki, M. (2003). An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons and Fractals, 18(1), 141–148.

    MathSciNet  MATH  Google Scholar 

  22. Çavuşoğlu, Ü., Panahi, S., Akgül, A., Jafari, S., & Kaçar, S. (2019). A new chaotic system with hidden attractor and its engineering applications: Analog circuit realization and image encryption. Analog Integrated Circuits and Signal Processing, 98(1), 85–99.

    Google Scholar 

  23. Mboupda Pone, J. R., Çiçek, S., Takougang Kingni, S., Tiedeu, A., & Kom, M. (2020). Passive–active integrators chaotic oscillator with anti-parallel diodes: Analysis and its chaos-based encryption application to protect electrocardiogram signals. Analog Integrated Circuits and Signal Processing, 103(1), 1–15.

    Google Scholar 

  24. Gokyildirim, A., Uyaroglu, Y., & Pehlivan, I. (2018). A weak signal detection application based on hyperchaotic lorenz system. Tehnicki Vjesnik, 25(3), 701–708.

    Google Scholar 

  25. Koyuncu, İ, Tuna, M., Pehlivan, İ, Fidan, C. B., & Alçın, M. (2020). Design, FPGA implementation and statistical analysis of chaos-ring based dual entropy core true random number generator. Analog Integrated Circuits and Signal Processing, 102(2), 445–456.

    Google Scholar 

  26. Li, Z., & Xu, D. (2004). A secure communication scheme using projective chaos synchronization. Chaos, Solitons and Fractals, 22(2), 477–481.

    MATH  Google Scholar 

  27. Bao, B. C., Xu, J. P., Zhou, G. H., Ma, Z. H., & Zou, L. (2011). Chaotic memristive circuit: Equivalent circuit realization and dynamical analysis. Chinese Physics B, 20(12), 1–7.

    Google Scholar 

  28. Rakkiyappan, R., Sivasamy, R., & Li, X. (2015). Synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique. Circuits, Systems, and Signal Processing, 34(3), 763–778.

    Google Scholar 

  29. Zhu, B., Fan, Q., Li, G., & Wang, D. (2021). Chaos suppression for a Buck converter with the memristive load. Analog Integrated Circuits and Signal Processing, 107(2), 309–318.

    Google Scholar 

  30. Itoh, M., & Chua, L. O. (2008). Memristor oscillators. International Journal of Bifurcation and Chaos, 18(11), 3183–3206.

    MathSciNet  MATH  Google Scholar 

  31. Sabarathinam, S., Volos, C. K., & Thamilmaran, K. (2017). Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator. Nonlinear Dynamics, 87(1), 37–49.

    Google Scholar 

  32. Ma, J., Chen, Z., Wang, Z., & Zhang, Q. (2015). A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium. Nonlinear Dynamics, 81(3), 1275–1288.

    MATH  Google Scholar 

  33. Xu, B., Wang, G., Iu, H. H. C., Yu, S., & Yuan, F. (2019). A memristor–meminductor-based chaotic system with abundant dynamical behaviors. Nonlinear Dynamics, 96(1), 765–788.

    MATH  Google Scholar 

  34. Hu, X., Chen, G., Duan, S., & Feng, G. (2014). A Memristor-Based Chaotic System with Boundary Conditions. Memristor Networks (pp. 351–364). Cham: Springer.

    Google Scholar 

  35. Pham, V. T., Volos, C. K., Vaidyanathan, S., Le, T. P., & Vu, V. Y. (2015). A Memristor-based hyperchaotic system with hidden attractors: Dynamics, synchronization and circuital emulating. Journal of Engineering Science and Technology Review, 8(2), 205–214.

    Google Scholar 

  36. Bao, H., Wang, N., Bao, B., Chen, M., Jin, P., & Wang, G. (2018). Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria. Communications in Nonlinear Science and Numerical Simulation, 57, 264–275.

    MathSciNet  MATH  Google Scholar 

  37. Wang, M., Deng, Y., Liao, X., Li, Z., Ma, M., & Zeng, Y. (2019). Dynamics and circuit implementation of a four-wing memristive chaotic system with attractor rotation. International Journal of Non-Linear Mechanics, 111, 149–159.

    Google Scholar 

  38. Li, C., Joo-Chen Thio, W., Ho-Ching, Iu., & H., & Lu, T. (2017). A memristive chaotic oscillator with increasing amplitude and frequency. IEEE Access, 6, 12945–12950.

    Google Scholar 

  39. Bao, B., Ma, Z., Xu, J., Liu, Z., & Xu, Q. (2011). A simple memristor chaotic circuit with complex dynamics. International Journal of Bifurcation and Chaos, 21(9), 2629–2645.

    MATH  Google Scholar 

  40. Li, Q., Zeng, H., & Li, J. (2015). Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria. Nonlinear Dynamics, 79(4), 2295–2308.

    MathSciNet  Google Scholar 

  41. Ma, X., Mou, J., Liu, J., Ma, C., Yang, F., & Zhao, X. (2020). A novel simple chaotic circuit based on memristor–memcapacitor. Nonlinear Dynamics, 100(3), 2859–2876.

    Google Scholar 

  42. Kountchou, M., Folifack Signing, V. R., Tagne Mogue, R. L., Kengne, J., & Saïdou. (2021). Complex dynamical behaviors in a memcapacitor–inductor circuit. Analog Integrated Circuits and Signal Processing, 106(3), 615–634.

    Google Scholar 

  43. Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196–1199.

    MathSciNet  MATH  Google Scholar 

  44. Kizmaz, H., Kocamaz, U. E., & Uyaroğlu, Y. (2019). Control of memristor-based simplest chaotic circuit with one-state controllers. Journal of Circuits, Systems and Computers, 28(01), 1950007.

    Google Scholar 

  45. Ge, C., Hua, C., & Guan, X. (2014). Master-slave synchronization criteria of Lur’e systems with time-delay feedback control. Applied Mathematics and Computation, 244, 895–902.

    MathSciNet  MATH  Google Scholar 

  46. Kuntanapreeda, S., & Sangpet, T. (2012). Synchronization of chaotic systems with unknown parameters using adaptive passivity-based control. Journal of the Franklin Institute, 349(8), 2547–2569.

    MathSciNet  MATH  Google Scholar 

  47. Agrawal, S. K., Srivastava, M., & Das, S. (2012). Synchronization of fractional order chaotic systems using active control method. Chaos, Solitons and Fractals, 45(6), 737–752.

    Google Scholar 

  48. Vaidyanathan, S., & Rasappan, S. (2014). Global chaos synchronization of n-scroll chua circuit and lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39(4), 3351–3364.

    MATH  Google Scholar 

  49. Muthuswamy, B. (2010). Implementing Memristor Based Chaotic Circuits. International Journal of Bifurcation and Chaos, 20(05), 1335–1350.

    MATH  Google Scholar 

  50. Muthuswamy, B., & Kokate, P. (2009). Memristor-based chaotic circuits. IETE Technical Review (Institution of Electronics and Telecommunication Engineers, India), 26(6), 417–429.

    Google Scholar 

  51. Wen, S., Zeng, Z., Huang, T., & Chen, Y. (2013). Fuzzy modeling and synchronization of different memristor-based chaotic circuits. Physics Letters, Section A: General, Atomic and Solid State Physics, 377(34–36), 2016–2021.

    MathSciNet  MATH  Google Scholar 

  52. Mezatio, B. A., Motchongom, M. T., Wafo Tekam, B. R., Kengne, R., Tchitnga, R., & Fomethe, A. (2019). A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability. Chaos, Solitons and Fractals, 120, 100–115.

    MathSciNet  MATH  Google Scholar 

  53. Chen, E., Min, L., & Chen, G. (2017). Discrete chaotic systems with one-line equilibria and their application to image encryption. International Journal of Bifurcation and Chaos. https://doi.org/10.1142/S0218127417500468

    Article  MATH  Google Scholar 

  54. Kengne, L. K., Kengne, J., & Fotsin, H. B. (2019). The effects of symmetry breaking on the dynamics of a simple autonomous jerk circuit. Analog Integrated Circuits and Signal Processing, 101(3), 489–512.

    Google Scholar 

  55. Gokyildirim, A., Uyaroglu, Y., & Pehlivan, I. (2016). A novel chaotic attractor and its weak signal detection application. Optik, 127(19), 7889–7895.

    Google Scholar 

  56. Wang, X., & Chen, G. (2012). A chaotic system with only one stable equilibrium. Communications in Nonlinear Science and Numerical Simulation, 17(3), 1264–1272.

    MathSciNet  Google Scholar 

  57. Nguomkam Negou, A., & Kengne, J. (2019). A minimal three-term chaotic flow with coexisting routes to chaos, multiple solutions, and its analog circuit realization. Analog Integrated Circuits and Signal Processing, 101(3), 415–429.

    Google Scholar 

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Acknowledgements

This work was supported by the Scientific Research Projects Coordination Unit of Bandırma Onyedi Eylül University (Project Number: BAP-20-1003-005).

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Bandırma Onyedi Eylül University, Bandırma, Balıkesir, Turkey

    Abdullah Gokyildirim & Abdullah Yesil

  2. Department of Electrical and Electronics Engineering, Erzincan Binali Yildirim University, Erzincan, Turkey

    Yunus Babacan

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  1. Abdullah Gokyildirim
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  2. Abdullah Yesil
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  3. Yunus Babacan
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Correspondence to Abdullah Gokyildirim.

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Gokyildirim, A., Yesil, A. & Babacan, Y. Implementation of a memristor-based 4D chaotic oscillator and its nonlinear control. Analog Integr Circ Sig Process 110, 91–104 (2022). https://doi.org/10.1007/s10470-021-01956-2

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