Advertisement

Nonlinear Dynamics

, Volume 93, Issue 4, pp 2057–2069 | Cite as

Crack synchronization of chaotic circuits under field coupling

  • Jun Ma
  • Fuqiang Wu
  • Ahmed Alsaedi
  • Jun Tang
Original Paper

Abstract

Nonlinear electric devices are important and essential for setting circuits so that chaotic outputs or periodical series can be generated. Chaotic circuits can be mapped into dimensionless dynamical systems by using scale transformation, and thus, synchronization control can be further investigated in numerical way. In case of synchronization approach, resistor is often used to bridge two chaotic circuits and gap junction connection is used to realize possible synchronization. In fact, complex electromagnetic effect in circuits should be considered when the capacitor and inductor (inductance coil) are attacked by high-frequency signals or noise-like disturbance. In this paper, two chaotic circuits are connected by using voltage coupling (via resistor) and triggering mutual induction electromotive force, which time-varying magnetic field is generated in the inductance coils. Therefore, magnetic field coupling is realized between two isolate inductance coils and induction electromotive force is generated to adjust the oscillation in circuits. It is found that field coupling can modulate the synchronization behaviors of chaotic circuits. In case of periodical oscillating state, the synchronization between two periodical circuits under voltage coupling is destroyed when field coupling is considered. Furthermore, the synchronization between chaotic circuits becomes more difficult when field coupling is triggered. Open problems for this topic are proposed for further investigation.

Keywords

Field coupling Chaotic circuit Synchronization Electromagnetic induction Memristor 

Notes

Acknowledgements

This project is supported by National Natural Science Foundation of China under Grants. 11672122, 11765011. The authors would like to thank Ms. Lulu Lu for her help in producing Fig. 3.

Compliance with ethical standard

Conflicts of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Chen, P., Yu, S.M., Zhang, X.Y., et al.: ARM-embedded implementation of a video chaotic secure communication via WAN remote transmission with desirable security and frame rate. Nonlinear Dyn. 86, 725–740 (2016)CrossRefGoogle Scholar
  2. 2.
    Gong, S.Q., Xing, C.W., Chen, S., et al.: Secure communications for dual-polarized MIMO systems. IEEE Trans. Signal Process. 65, 4177–4192 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Wu, X.J., Wang, H., Lu, H.T.: Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication. Nonlinear Anal. Real 13, 1441–1450 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Tlelo-Cuautle, E., de la Fraga, L.G., Viet-Thanh, P., et al.: Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points. Nonlinear Dyn. 89, 1129–1139 (2017)CrossRefGoogle Scholar
  5. 5.
    Hassan, M.F.: Synchronization of uncertain constrained hyperchaotic systems and chaos-based secure communications via a novel decomposed nonlinear stochastic estimator. Nonlinear Dyn. 83, 2183–2211 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Xie, E.Y., Li, C.Q., Yu, S.M., et al.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)CrossRefGoogle Scholar
  7. 7.
    Li, X.W., Li, C.Q., Lee, I.K.: Chaotic image encryption using pseudo-random masks and pixel mapping. Signal Process. 125, 48–63 (2016)CrossRefGoogle Scholar
  8. 8.
    Ye, G.D., Zhao, H.Q., Chai, H.J., et al.: Chaotic image encryption algorithm using wave-line permutation and block diffusion. Nonlinear Dyn. 83, 2067–2077 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Abderrahim, N.W., Benmansour, F.Z., Seddiki, O.: A chaotic stream cipher based on symbolic dynamic description and synchronization. Nonlinear Dyn. 78, 197–207 (2014)CrossRefGoogle Scholar
  10. 10.
    Muthukumar, P., Balasubramaniam, P., Ratnavelu, K.: Synchronization and an application of a novel fractional order King Cobra chaotic system. Chaos 24, 033105 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Yang, X.P., Min, L.Q., Wang, X.: A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption. Chaos 25, 053104 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Volos, C., Akgul, A., Viet-Thanh, P., et al.: A simple chaotic circuit with a hyperbolic sine function and its use in a sound encryption scheme. Nonlinear Dyn. 89, 1047–1061 (2017)CrossRefGoogle Scholar
  13. 13.
    Koyuncu, I., Ozcerit, A.T.: The design and realization of a new high speed FPGA-based chaotic true random number generator. Comput. Electr. Eng. 58, 203–214 (2017)CrossRefGoogle Scholar
  14. 14.
    Acosta, A.J., Addabbo, T., Tena-Sanchez, E.: Embedded electronic circuits for cryptography, hardware security and true random number generation: an overview. Int. J. Circuit Theory Appl. 45, 145–169 (2017)CrossRefGoogle Scholar
  15. 15.
    Murillo-Escobar, M.A., Cruz-Hernandez, C., Cardoza-Avendano, L., et al.: A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn. 87, 407–425 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Li, C.Q., Liu, Y.S., Xie, T., et al.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dyn. 73, 2083–2089 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197(4300), 287–289 (1977)CrossRefzbMATHGoogle Scholar
  18. 18.
    Rössler, O.E.: An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)CrossRefzbMATHGoogle Scholar
  19. 19.
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Skarda, C.A., Freeman, W.J.: How brains make chaos in order to make sense of the world. Behav. Brain Sci. 10(2), 161–173 (1987)CrossRefGoogle Scholar
  21. 21.
    Grebogi, C., Ott, E., Yorke, J.A.: Crises, sudden changes in chaotic attractors, and transient chaos. Physica D 7(1–3), 181–200 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Tabor, M.: Chaos and Integrability in Nonlinear Dynamics: An Introduction. Wiley, New York (1989)zbMATHGoogle Scholar
  23. 23.
    He, Z.M., La, X.: Bifurcation and chaotic behavior of a discrete-time predator–prey system. Nonlinear Anal. Real 12, 403–417 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ma, J., Wang, Q.Y., Jin, W.Y., et al.: Control chaos in Hindmarsh–Rose neuron by using intermittent feedback with one variable. Chin. Phys. Lett. 25, 3582–3585 (2008)CrossRefGoogle Scholar
  25. 25.
    Wang, C.N., Chu, R.T., Ma, J.: Controlling a chaotic resonator by means of dynamic track control. Complexity 21, 370–378 (2015)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Ma, J., Wu, F.Q., Jin, W.Y., et al.: Calculation of Hamilton energy and control of dynamical systems with different types of attractors. Chaos 27, 053108 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Rajagopal, K., Vaidyanathan, S., Karthikeyan, A., et al.: Dynamic analysis and chaos suppression in a fractional order brushless DC motor. Electr. Eng. 99, 721–723 (2017)CrossRefGoogle Scholar
  28. 28.
    Messadi, M., Mellit, A.: Control of chaos in an induction motor system with LMI predictive control and experimental circuit validation. Chaos Solitons Fractals 97, 51–58 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Karthikeyan, A., Rajagopal, K.: Chaos control in fractional order smart grid with adaptive sliding mode control and genetically optimized PID control and its FPGA implementation. Complexity 2017, 3815146 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Tacha, O.I., Volos, C.K., Kyprianidis, I.M., et al.: Analysis, adaptive control and circuit simulation of a novel nonlinear finance system. Appl. Math. Comput. 276, 200–217 (2016)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Wang, C.N., He, Y.J., Ma, J., et al.: Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems. Complexity 20, 64–73 (2014)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wang, Z.L., Wang, C., Shi, X.R., et al.: Realizing hybrid synchronization of time-delay hyperchaotic 4D systems via partial variables. Appl. Math. Comput. 245, 427–437 (2014)MathSciNetzbMATHGoogle Scholar
  33. 33.
    Lee, S., Park, M., Baek, J.: Robust adaptive synchronization of a class of chaotic systems via fuzzy bilinear observer using projection operator. Inf. Sci. 402, 182–198 (2017)CrossRefGoogle Scholar
  34. 34.
    Liu, K.X., Wu, L.L., Lu, J.H., et al.: Finite-time adaptive consensus of a class of multi-agent systems. Sci. China Technol. Sci. 59, 22–32 (2016)CrossRefGoogle Scholar
  35. 35.
    Zhang, H.W., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatic 48, 1432–1439 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Ma, J., Wu, X.Y., Chu, R.T., et al.: Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dyn. 76, 1951–1962 (2014)CrossRefGoogle Scholar
  37. 37.
    Alombah, N.H., Fotsin, H., Romanic, K.: Coexistence of multiple attractors. Metastable chaos and bursting oscillations in a multiscroll memristive chaotic circuit. Int. J. Bifurc. Chaos 27, 1750067 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Escalante-Gonzalez, R.J., Campos-Canton, E., Nicol, M.: Generation of multi-scroll attractors without equilibria via piecewise linear systems. Chaos 27, 053109 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Viet-Thanh, P., Volos, C., Jafari, S., et al.: A chaotic system with different families of hidden attractors. Int. J. Bifurc. Chaos 26, 1650139 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Dudkowski, D., Jafari, S., Kapitaniak, T., et al.: Hidden attractors in dynamical systems. Phys. Rep. 637, 1–50 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Zhou, L., Wang, C.N., Zhou, L.L.: Generating hyperchaotic multi-wing attractor in a 4D memristive circuit. Nonlinear Dyn. 85, 2653–2663 (2016)CrossRefGoogle Scholar
  42. 42.
    Zhang, C.X.: Theoretical design and circuit realization of complex grid multi-wing chaotic system. Optik 127, 4584–4589 (2016)CrossRefGoogle Scholar
  43. 43.
    Grassi, G., Severance, F.L., Miller, D.A.: Multi-wing hyperchaotic attractors from coupled Lorenz systems. Chaos Solitons Fractals 41, 284–291 (2009)CrossRefzbMATHGoogle Scholar
  44. 44.
    Ma, J., Wu, F.Q., Ren, G.D., et al.: A class of initials-dependent dynamical systems. Appl. Math. Comput. 298, 65–76 (2017)MathSciNetGoogle Scholar
  45. 45.
    Ren, G.D., Wu, G., Ma, J., et al.: Simulation of electric activity of neuron by setting up a reliable neuronal circuit driven by electric autapse. Acta Phys. Sin. 64, 058702 (2015). In ChineseGoogle Scholar
  46. 46.
    Wu, X.Y., Ma, J., Yuan, L.H., et al.: Simulating electric activities of neurons by using PSPICE. Nonlinear Dyn. 75, 113–126 (2014)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Korkmaz, N., Ozturk, I., Kilic, R.: The investigation of chemical coupling in a HR neuron model with reconfigurable implementations. Nonlinear Dyn. 86, 1841–1854 (2016)CrossRefGoogle Scholar
  48. 48.
    Ren, G.D., Zhou, P., Ma, J., et al.: Dynamical response of electrical activities in digital neuron circuit driven by autapse. Int. J. Bifurc. Chaos 27, 1750287 (2017)MathSciNetGoogle Scholar
  49. 49.
    Majhi, S., Perc, M., Ghosh, D.: Chimera states in a multilayer network of coupled and uncoupled neurons. Chaos 27, 073109 (2017)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Majhi, S., Perc, M., Ghosh, D.: Chimera states in uncoupled neurons induced by a multilayer structure. Sci. Rep. 6, 39033 (2016)CrossRefGoogle Scholar
  51. 51.
    Wang, C.N., Lv, M., Alsaedi, A., et al.: Synchronization stability and pattern selection in a memristive neuronal network. Chaos 27, 113108 (2017)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Wu, F.Q., Wang, C.N., Jin, W.Y., et al.: Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Physica A 469, 81–88 (2017)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Ma, J., Mi, L., Zhou, P., et al.: Phase synchronization between two neurons induced by coupling of electromagnetic field. Appl. Math. Comput. 307, 321–328 (2017)MathSciNetGoogle Scholar
  54. 54.
    Ma, J., Wu, F.Q., Wang, C.N.: Synchronization behaviors of coupled neurons under electromagnetic radiation. Int. J. Mod. Phys. B 31, 1650251 (2017)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Wang, Y., Ma, J., Xu, Y., et al.: The electrical activity of neurons subject to electromagnetic induction and Gaussian white noise. Int. J. Bifurc. Chaos 27, 1750030 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Corinto, F., Ascoli, A., Gilli, M.: Nonlinear dynamics of memristor oscillators. IEEE Trans. Circuits Syst. I(58), 1323–1336 (2011)MathSciNetCrossRefGoogle Scholar
  57. 57.
    Zhang, G., Ma, J., Alsaedi, A., et al.: Dynamical behavior and application in Josephson Junction coupled by memristor. Appl. Math. Comput. 321, 290–299 (2018)MathSciNetGoogle Scholar
  58. 58.
    Xu, Y., Jia, Y., Ma, J., et al.: Synchronization between neurons coupled by memristor. Chaos Solitons Fractals 104, 435–442 (2017)CrossRefGoogle Scholar
  59. 59.
    Tamasevicius, A., Namajunas, A., Cenys, A.: Simple 4D chaotic oscillator. Electr. Lett. 32, 957–958 (1996)CrossRefGoogle Scholar
  60. 60.
    Sprott, J.C.: Simple chaotic systems and circuits. Am. J. Phys. 68, 758–763 (2000)CrossRefGoogle Scholar
  61. 61.
    Ren, G.D., Xu, Y., Wang, C.N., et al.: Synchronization behavior of coupled neuron circuits composed of memristors. Nonlinear Dyn. 88, 893–901 (2017)CrossRefGoogle Scholar
  62. 62.
    Guo, S.L., Xu, Y., Wang, C.N., et al.: Collective response, synapse coupling and field coupling in neuronal network. Chaos Solitons Fractals 105, 120–127 (2017)MathSciNetCrossRefGoogle Scholar
  63. 63.
    Wu, J., Xu, Y., Ma, J.: Levy noise improves the electrical activity in a neuron under electromagnetic radiation. PLoS One 12, e0174330 (2017)CrossRefGoogle Scholar
  64. 64.
    Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)CrossRefGoogle Scholar
  65. 65.
    Xu, Y., Ying, H.P., Jia, Y., et al.: Autaptic regulation of electrical activities in neuron under electromagnetic induction. Sci. Rep. 7, 43452 (2017)CrossRefGoogle Scholar
  66. 66.
    Wu, F.Q., Wang, C.N., Xu, Y., et al.: Model of electrical activity in cardiac tissue under electromagnetic induction. Sci. Rep. 6, 28 (2016)CrossRefGoogle Scholar
  67. 67.
    Ma, J., Wu, F.Q., Hayat, T., et al.: Electromagnetic induction and radiation-induced abnormality of wave propagation in excitable media. Physica A 486, 508–516 (2017)MathSciNetCrossRefGoogle Scholar
  68. 68.
    Wang, C.N., Ma, J.: A review and guidance for pattern selection in spatiotemporal system. Int. J. Mod. Phys. B 32, 1830003 (2018)MathSciNetCrossRefGoogle Scholar
  69. 69.
    Wolf, A., Swift, J.B., Swinney, H.L., et al.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsLanzhou University of TechnologyLanzhouChina
  2. 2.College of Electrical and Information EngineeringLanzhou University of TechnologyLanzhouChina
  3. 3.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  4. 4.Department of PhysicsChina University of Mining and TechnologyXuzhouChina

Personalised recommendations