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A novel approach for generating multi-direction multi-double-scroll attractors

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Abstract

It is a common phenomenon that multi-scroll attractors are realized by introducing the various nonlinear functions with multiple breakpoints in double-scroll chaotic systems. Differently, this paper introduces a new systematic method for generating multi-direction multi-double-scroll (MDMDS) chaotic attractors without changing the original nonlinear functions. By using the multi-pulse control technique in a three-dimensional double-scroll chaos system, a new family of double-scroll grid attractors can be generated, including 1-D double-scroll, 2-D double-scroll, and 3-D double-scroll chaotic attractors. Theoretical analysis and numerical simulations show the MDMDS can be generated by constructing pulsed excitation in corresponding state variable directions (1-D), plane (2-D), or space (3-D). Mean while, it is possible to increase the number of scrolls in all state variable directions by adding the number of pulsed excitation. Furthermore, the proposed approach is applied in Chua’s circuit; a series of MDMDS attractors are presented. Finally, corresponding realization circuit is designed using CFOAs. The obtained Pspice results are in agreement with numerical simulation results, which verify the availability and feasibility of this method.

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References

  1. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  2. Wang, X., Luo, C.: Researches on chaos phenomenon of EEG dynamics model. Appl. Math. Comput. 183, 30–41 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Li, C., Liu, Y., Xie, T., Chen, M.Z.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dyn. 73, 2083–2089 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Li, K.Z., Zhao, M.C., Fu, X.C.: Projective synchronization of driving-response systems and its application to secure communication. IEEE Trans. Circuits Syst. I, Reg. Papers 56, 2280–2291 (2009)

    Article  MathSciNet  Google Scholar 

  5. Li, C.: Cracking a hierarchical chaotic image encryption algorithm based on permutation. Signal Process. 118, 203–210 (2016)

    Article  Google Scholar 

  6. Ginarsa, I.M., Soeprijanto, A., Purnomo, M.H.: Controlling chaos and voltage collapse using an ANFIS-based composite controller-static var compensator in power systems. Int. J. Elect. Power Energy Syst. 46, 79–88 (2013)

    Article  Google Scholar 

  7. Wang, Q., Yu, S., Li, C., Lü, J., Fang, X., Guyeux, C., Bahi, J.M.: Theoretical design and FPGA-based implementation of higher-dimensional digital chaotic systems. IEEE Trans. on Circuits and Syst. I: Reg. Papers 63, 401–412 (2016)

    Article  MathSciNet  Google Scholar 

  8. Shen, C., Yu, S., Lü, J., Chen, G.: A systematic methodology for constructing hyperchaotic systems with multiple positive Lyapunov exponents and circuit implementation. IEEE Trans. Circuits Syst. I, Reg. Papers 61, 854–864 (2014)

    Article  Google Scholar 

  9. Lü, J., Han, F., Yu, X., Chen, G.: Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method. Automatica 40, 1677–1687 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Grassi, G., Severance, F.L., Miller, D.A.: Multi-wing hyperchaotic attractors from coupled Lorenz systems. Chaos, Solitons and Fractals 41, 284–291 (2009)

    Article  MATH  Google Scholar 

  11. Yu, S., Lü, J., Chen, G., Yu, X.: Design and implementation of grid multiwing butterfly chaotic attractors from a piecewise Lorenz system. IEEE Trans. Circuits Syst. II: Exp. Brief 57, 803–807 (2010)

    Article  Google Scholar 

  12. Yu, S., Lü, J., Chen, G., Yu, X.: Generating grid multiwing chaotic attractors by constructing heteroclinic loops into switching systems. IEEE Trans. Circuits Syst. II Exp. Brief 58, 314–318 (2011)

    Article  Google Scholar 

  13. Khan, M., Shah, T., Mahmood, H., Gondal, M.A.: An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71, 489–492 (2013)

    Article  MathSciNet  Google Scholar 

  14. Han, F., Hu, J.H., Yu, X., Wang, Y.: Fingerprint images encryption via multi-scroll chaotic attractors. Appl. Math. Comput. 185, 931–939 (2007)

    MATH  Google Scholar 

  15. Solak, E., Rhouma, R., Belghith, S.: Cryptanalysis of a multi-chaotic systems based image cryptosystem. Opt. Commun. 283, 232–236 (2010)

    Article  MATH  Google Scholar 

  16. Hu, J., Han, F.: A pixel-based scrambling scheme for digital medical images protection. J. Netw. Comput. Appl. 32, 788–794 (2009)

    Article  Google Scholar 

  17. Gmez-Guzmn, L., Cruz-Hernndez, C., Lpez-Gutirrez, R.M., Garca-Guerrero, E.E.: Synchronization of Chuas circuits with multi-scroll attractors: application to communication. Commun. Nonlinear Sci. 14, 2765–2775 (2009)

    Article  Google Scholar 

  18. Lin, Z., Yu, S., Lü, J., Cai, S., Chen, G.: Design and ARM-embedded implementation of a chaotic map-based real-time secure video communication system. IEEE Trans. Circuits Syst. Video Technol. 25, 1203–1216 (2015)

    Article  Google Scholar 

  19. Suykens, J.A., Vandewalle, J.: Generation of n-double scrolls (n= 1,2, 3, 4,). IEEE Trans. Circuits Syst. I Fundam. TheoryAppl. 40, 861–867 (1993)

    Article  MATH  Google Scholar 

  20. Suykens, J.A., Huang, A.: A family of n-scroll attractors from a generalized Chua’s circuit. Archiv fur Elektronik und Ubertragungstechnik 51, 131–137 (1997)

    Google Scholar 

  21. Yu, S., Tang, W.K., Lü, J., Chen, G.: Generation of-wing lorenz-like attractors from a modified Shimizu-Morioka model. IEEE Trans. Circuits Syst. II: Exp. Brief 55, 1168–1172 (2008)

    Article  Google Scholar 

  22. Ma, Y., Li, Y., Jiang, X.: Simulation and circuit implementation of 12-scroll chaotic system. Chaos, Soliton & Fractals 75, 127–133 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Snchez-Lpez, C., Trejo-Guerra, R., Munoz-Pacheco, J.M., Tlelo-Cuautle, E.: N-scroll chaotic attractors from saturated function series employing CCII+s. Nonlinear Dyn. 61, 331–341 (2010)

    Article  MATH  Google Scholar 

  24. Zuo, T., Sun, K., Ai, X., Wang, H.: High-order grid multiscroll chaotic attractors generated by the second-generation current conveyor circuit. IEEE Trans. Circuits Syst. II: Exp. Brief 61, 818–822 (2014)

    Article  Google Scholar 

  25. Wang, F., Liu, C.X.: Generation of multi-scroll chaotic attractors via the saw-tooth function. Int. J. Mod. Phys. B 22, 2399–2405 (2008)

    Article  Google Scholar 

  26. Bao, B., Zhou, G., Xu, J., Liu, Z.: Multiscroll chaotic attractors from a modified colpitts oscillator model. Int. J. Mod. Phys. B 20, 2203–2211 (2010)

    MathSciNet  MATH  Google Scholar 

  27. Yu, S., Tang, W.K., Chen, G.: Generation of nm-scroll attractors under a Chua-circuit framework. Int. J. Bifurc. Chaos 17, 3951–3964 (2007)

    Article  MATH  Google Scholar 

  28. Yu, S., Tang, W.K.: Generation of nm-scroll attractors in a two-port RCL network with hysteresis circuits. Chaos, Solitons and Fractals 39, 821–830 (2009)

    Article  MATH  Google Scholar 

  29. Lü, J., Chen, G., Yu, X., Leung, H.: Design and analysis of multiscroll chaotic attractors from saturated function series. IEEE Trans. Circuits Syst. I(51), 2476–2490 (2004)

    Article  MathSciNet  Google Scholar 

  30. Li, F., Yao, C.G.: The infinite-scroll attractor and energytransition in chaotic circuit. Nonlinear Dyn. 84, 2305C2315 (2016)

    Google Scholar 

  31. Ma, J., Wu, X., Chu, R., Zhang, L.: Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice. Nonlinear Dyn. 76, 1951–1962 (2014)

    Article  Google Scholar 

  32. Lü, J., Chen, G.: Generating multiscroll chaotic attractors: theories, methods and applications. Int. J. Bifurc. Chaos 06, 775–858 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yalcin, M.E., Suykens, J.A., Vandewalle, J., Ozoguz, S.: Families of scroll grid attractors. Int. J. Bifurc. Chaos 12, 23–41 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  34. Munoz-Pacheco, J.M., Zambrano-Serrano, E., Flix-Beltrn, O., Gmez-Pavn, L.C., Luis-Ramos, A.: Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems. Nonlinear Dyn. 70, 1633–1643 (2012)

    Article  MathSciNet  Google Scholar 

  35. Munoz-Pacheco, J.M., Tlelo-Cuautle, E., Toxqui-Toxqui, I., Snchez-Lpez, C., Trejo-Guerra, R.: Frequency limitations in generating multi-scroll chaotic attractors using CFOAs. Int. J. Elec. 101, 1559–1569 (2014)

    Article  Google Scholar 

  36. Yalcin, M.E., Suykens, J.A.K., Vandewalle, J.: Cellular Neural Networks, Multi-Scroll Chaos and Synchronization. World Scientific, Singapore (2005)

    Book  MATH  Google Scholar 

  37. Lü, J., Yu, X., Chen, G.: Generating chaotic attractors with multiple merged basins of attraction: a switching piecewise-linear control approach. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50, 198–207 (2003)

    Article  MathSciNet  Google Scholar 

  38. Lü, J., Yu, S., Leung, H., Chen, G.: Experimental verification of multidirectional multiscroll chaotic attractors. IEEE Trans. Circuits Syst. I, Reg. Papers 53, 149–165 (2006)

  39. Deng, W., Lü, J.: Design of multidirectional multiscroll chaotic attractors based on fractional differential systems via switching control. Chaos 16, 043120 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  40. Sprott, J.C.: A new class of chaotic circuit. Phys. Lett. A 266, 19–23 (2000)

    Article  Google Scholar 

  41. Chua, L.O., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circuits Syst. 33, 1072–1118 (1986)

    Article  MATH  Google Scholar 

  42. Elwakil, A.S., Kennedy, M.P.: Improved implementation of Chua’s chaotic oscillator using current feedback op amp. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47, 76–79 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

We thank Prof. Xiaoping Wang at Huazhong University of Science and Technology for valuable assistance and appreciate suggestions on the manuscript. The work is supported by the State Key Program of the National Natural Science Foundation of China (Grant No. 61134012), the National Natural Science Foundation of China (Grant Nos. 11271146, 61374150 and 61471310), the Science and Technology Program of Wuhan (Grant No. 20130105010117).

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Authors and Affiliations

  1. School of Actomatic, Huazhong University of Science and Technology, Wuhan, 430074, China

    Qinghui Hong

  2. Wuhan National Laboratory for Optelectronics, Wuhan, 430074, China

    Qinghui Hong, Qingguo Xie & Peng Xiao

  3. School of Physics and Optoelectronics, Xiangtan University, Xiangtan, 411105, China

    Qinghui Hong

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  1. Qinghui Hong
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  2. Qingguo Xie
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  3. Peng Xiao
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Correspondence to Qinghui Hong.

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Hong, Q., Xie, Q. & Xiao, P. A novel approach for generating multi-direction multi-double-scroll attractors. Nonlinear Dyn 87, 1015–1030 (2017). https://doi.org/10.1007/s11071-016-3094-5

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