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A 2-D conditional symmetric hyperchaotic map with complete control

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Abstract

By introducing an absolute value function for polarity balance, a unique hyperchaotic map with complete control and conditional symmetry is designed. Firstly, coexisting conditional symmetric bifurcations and hyperchaotic phase trajectories are found in the map. Then, two independent parameters are proven to provide a direct knob for partial and total amplitude control. Finally, a STM32-based hardware experiment is carried out to verify the theoretical finding.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Zhang, Y., Xu, Y., Yao, Z., Ma, J.: A feasible neuron for estimating the magnetic field effect. Nonlinear Dyn. 102, 1849–1867 (2020)

    Article  Google Scholar 

  2. Xu, Y., Guo, Y., Ren, G., Ma, J.: Dynamics and stochastic resonance in a thermosensitive neuron. Appl. Math. Comput. 385, 125427 (2020)

    MathSciNet  MATH  Google Scholar 

  3. Wang, C., Liu, Z., Hobiny, A., Xu, W., Ma, J.: Capturing and shunting energy in chaotic Chua circuit. Chaos, Solitons Fractals 134, 109697 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Liu, Y., Xu, Y., Ma, J.: Synchronization and spatial patterns in a light-dependent neural network. Commun. Nonlinear Sci. Numer. Simulat. 89, 105297 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hua, Z., Zhou, B., Zhou, Y.: Sine chaotification model for enhancing chaos and its hardware implementation. IEEE Trans. Indus. Electron. 66(2), 1273–1284 (2019)

    Article  MathSciNet  Google Scholar 

  6. Zhu, S., Zhou, J., Chen, G., Lu, J.A.: A new method for topology identification of complex dynamical networks. IEEE Trans. Cybern. 51(4), 2224–2231 (2019)

    Article  Google Scholar 

  7. Li, C., Sprott, J.C., Akgul, A., Iu, H.C., Zhao, Y.: A new chaotic oscillator with free control. Chaos 27(8), 083101 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, C., Sprott, J.C., Yuan, Z., Li, H.: Constructing chaotic systems with total amplitude control. Int. J. Bifurcat. Chaos. 25(10), 1530025 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhou, X., Li, C., Li, Y., Lu, X., Lei, T.: An amplitude-controllable 3-d hyperchaotic map with homogenous multistability. Nonlinear Dyn. 58, 61 (2021)

    Google Scholar 

  10. Kong, S., Li, C., Jiang, H., Lai, Q., Jiang, X.: A 2d hyperchaotic map with conditional symmetry and attractor growth. Chaos. 31(4), 043121 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang, Y., Blum, R.S.: Mimo radar waveform design based on mutual information and minimum mean-square error estimation. IEEE Trans. Signal Process. 43(1), 330–343 (2007)

    Google Scholar 

  12. Li, C., Sprott, J.C., Xing, H.: Constructing chaotic systems with conditional symmetry. Nonlinear Dyn. 87(2), 1351–1358 (2016)

    Article  MATH  Google Scholar 

  13. Li, C., Sun, J., Lu, T., Sprott, J.C., Liu, Z.: Polarity balance for attractor self-reproducing. Chaos 30(6), 063144 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, C., Xu, Y., Chen, G., Liu, Y., Zheng, J.: Conditional symmetry: Bond for attractor growing. Nonlinear Dyn. 95(2), 1245–1256 (2018)

    Article  MATH  Google Scholar 

  15. Zhang, S., Li, C., Zheng, J., Wang, X., Zeng, Z., Peng, X.: Generating any number of initial offset-boosted coexisting chua’s double-scroll attractors via piecewise-nonlinear memristor. IEEE Trans. Indus. Electron. 36, 2116 (2021)

    Google Scholar 

  16. Zhang, S., Zheng, J., Wang, X., Zeng, Z., He, S.: Initial offset boosting coexisting attractors in memristive multi-double-scroll hopfield neural network. Nonlinear Dyn. 102(4), 2821–2841 (2020)

    Article  Google Scholar 

  17. Zhang, L., Liu, Y., Wei, Z., Jiang, H., Bi, Q.: A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors. Chin. Phys. B. 29(6), 060501 (2020)

    Article  Google Scholar 

  18. Sprott, J.C., Wang, X., Chen, G.: Coexistence of point, periodic and strange attractors. Int. J. Bifurcat. Chaos. 23(05), 1350093 (2013)

    Article  MathSciNet  Google Scholar 

  19. Jafari, S., Sprott, J.C.: Simple chaotic flows with a line equilibrium. Chaos Soliton. Fract. 57, 79–84 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Jiang, H., Liu, Y., Wei, Z., Zhang, L.: Hidden chaotic attractors in a class of two-dimensional maps. Nonlinear Dyn. 85(4), 2719–2727 (2016)

    Article  MathSciNet  Google Scholar 

  21. Zhang, S., Wang, X., Zeng, Z.: A simple no-equilibrium chaotic system with onlyone signum function for generating multidirectional variable hidden attractors and its hardware implementation. Chaos. 30(5), 053129 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hua, Z., Yi, S., Zhou, Y., Li, C., Wu, Y.: Designing hyperchaotic cat maps with any desired number of positive lyapunov exponents. IEEE Trans. Cybern. 48(2), 463–473 (2018)

    Article  Google Scholar 

  23. Min, F., Luo, A.: Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints. Chaos Soliton Fract 45(7), 998–1011 (2012)

    Article  MATH  Google Scholar 

  24. Lin, H., Wang, C., Yu, F., Xu, C., Hong, Q., Yao, W., Sun, Y.: An ex-tremely simple multiwing chaotic system:dynamics analysis, encryption application, and hardware implementation. IEEE Trans. Indus. Electron. 68(12), 12708 (2021)

    Article  Google Scholar 

  25. Peng, Y., Sun, K., He, S.: A discrete memristor model and its application in henon map. Chaos Soliton Fract. 137, 109873 (2020)

    Article  MATH  Google Scholar 

  26. Panahi, S., Sprott, J.C., Jafari, S.: Two simplest quadratic chaotic maps without equilibrium. Int. J. Bifurcat. Chaos. 28(12), 1850144 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  27. Frederickson, P., Kaplan, J., Yorke, E., Yorke, J.: The liapunov dimension of strange attractors. J. Diff. Eq. 49(2), 185–207 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica. 16(3), 285–317 (1985)

    MathSciNet  MATH  Google Scholar 

  29. Wang, Z.P., Wu, H.N.: On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach. IEEE Trans. Cybern. 45(4), 819–829 (2015)

    Article  Google Scholar 

  30. Li, Y., Li, C., Zhang, S., Chen, G., Zeng, Z.: A self-reproduction hyperchaotic map with compound lattice dynamics. IEEE Trans. Indus. Electron. 69(10), 10564–10572 (2022)

    Article  Google Scholar 

  31. Li, Y., Li, C., Zhao, Y., Liu, S.: Memristor-type chaotic mapping. Chaos 32(2), 021104 (2022)

    Article  MathSciNet  Google Scholar 

  32. Zhang, H., Ma, T., Huang, G.B., Wang, C.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dualstage impulsive control. IEEE Trans. Syst. Man, Cybern. 40(3), 831–844 (2010)

    Article  Google Scholar 

  33. Lai, Q., Benyamin, N., Feng, L.: Dynamic analysis, circuit realization, control design and image encryption application of an extended lü system with coexisting attractors. Chaos Soliton Fract. 114, 230–245 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  34. Wang, T., Song, L., Wang, M., Zhuang, Z.: A novel image encryption algorithm based on parameter-control scroll chaotic attractors. IEEE Access. 8, 8034196 (2020)

    Google Scholar 

  35. Zhou, Y., Hua, Z., Pun, C.M., Chen, C.L.: Cascade chaotic system with applications. IEEE Trans. Cybern. 45(9), 2001–2012 (2015)

    Article  Google Scholar 

  36. Lin, H., Wang, C., Hong, Q., Sun, Y.: A multi-stable memristor and its application in a neural network. IEEE Trans. Circuits Syst. II: Expr. Briefs. 67(12), 3472–3476 (2020)

    Article  Google Scholar 

  37. Zhang, X., Wu, F., Ma, J., Hobiny, A., Alzahrani, F., Ren, G.: Field coupling synchronization between chaotic circuits via a memristor. Int J Electron Commun. (AEU) 115,153050 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported financially by the National Natural Science Foundation of China (Grant No. 61871230).

Author information

Authors and Affiliations

  1. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yongxin Li & Chunbiao Li

  2. School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yongxin Li & Chunbiao Li

  3. School of Life Science, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Sicong Liu

  4. School of Computer Science and Technology, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, 518055, China

    Zhongyun Hua

  5. School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, 224002, China

    Haibo Jiang

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  1. Yongxin Li
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  2. Chunbiao Li
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  3. Sicong Liu
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  4. Zhongyun Hua
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  5. Haibo Jiang
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Correspondence to Chunbiao Li.

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Li, Y., Li, C., Liu, S. et al. A 2-D conditional symmetric hyperchaotic map with complete control. Nonlinear Dyn 109, 1155–1165 (2022). https://doi.org/10.1007/s11071-022-07485-5

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  • DOI: https://doi.org/10.1007/s11071-022-07485-5

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