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A simple meminductor-based chaotic system with complicated dynamics

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Abstract

In this paper, we propose a novel meminductor model for exploring its characteristics. By using this model, a simple meminductor-based circuit with three elements is constructed. Stability and dynamical behaviors of the circuit are investigated in detail. The study finds that the system has complicated nonlinear phenomena, such as coexisting bifurcation modes, coexisting attractors, and two different kinds of chaotic transients. Furthermore, by the circuit experiment, the chaotic characteristics of the system are confirmed, which illustrates the validity of the theoretical analysis.

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References

  1. Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1724 (2009)

    Article  Google Scholar 

  4. Rabbani, P., Dehghani, R., Shahpari, N.: A multilevel memristor-CMOS memory cell as a ReRAM. Microelectron. J. 46, 1283–1290 (2015)

    Article  Google Scholar 

  5. Wen, S.P., Zeng, Z.G., Huang, T.W., Zhang, Y.D.: Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators. IEEE Trans. Fuzzy Syst. 22, 1704–1713 (2014)

    Article  Google Scholar 

  6. Lv, M., Wang, C.N., Tang, J., Ma, J.: Collapse of synchronization in a memristive network. Commun. Theor. Phys. 64, 659–664 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lv, M., Wang, C.N., Ren, G.D., Ma, J., Song, X.L.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)

    Article  Google Scholar 

  8. Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)

    Article  Google Scholar 

  9. Pham, V.T., Jafari, S., Vaidyanathan, S., Volos, C., Wang, X.: A novel memristive neural network with hidden attractors and its circuitry implementation. Sci. China Technol. Sci. 59, 358–363 (2016)

    Article  Google Scholar 

  10. Wen, S.P., Zeng, Z.G., Huang, T.W., Li, C.J.: Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays. Int. J. Robust Nonlinear Control 25, 610–624 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wen, S.P., Huang, T.W., Yu, X.H., Chen, M.Z.Q., Zeng, Z.G.: Sliding-mode control of memristive Chua’s systems via the event-based method. IEEE Trans. Circuits Syst. II Exp. Briefs 64, 81–85 (2017)

    Article  Google Scholar 

  12. Wang, G.Y., Cai, B.Z., Jin, P.P., Hu, T.L.: Memcapacitor model and its application in a chaotic oscillator. Chin. Phys. B 25, 010503 (2016)

    Article  Google Scholar 

  13. Fouda, M.E., Radwan, A.G.: Resistive-less memcapacitor-based relaxation oscillator. Int. J. Circuit. Theor. Appl. 43, 959–965 (2015)

    Article  Google Scholar 

  14. Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, H., Sah, M.P., Yang, C., Cho, S., Chua, L.O.: Memristor emulator for memristor circuit applications. IEEE Trans. Circuits Syst. I Regul. Pap. 59, 2422–2431 (2012)

    Article  MathSciNet  Google Scholar 

  16. Bao, B.C., Jiang, P., Wu, H.G., Hu, F.W.: Complex transient dynamics in periodically forced memristive Chua’s circuit. Nonlinear Dyn. 79, 2333–2343 (2015)

  17. Itoh, M., Chua, L.O.: Dynamics of memristor circuits. Int. J. Bifurc. Chaos 24, 1430015 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang, G.Y., Cui, M.Z., Cai, B.Z., Wang, X.Y., Hu, T.L.: A chaotic oscillator based on HP memristor model. Math. Probl. Eng. (2015). doi:10.1155/2015/561901

  19. Yuan, F., Wang, G.Y., Wang, X.Y.: Dynamical characteristics of HP memristor based on equivalent circuit model in chaotic oscillator. Chin. Phys. B 24, 060506 (2015)

    Article  Google Scholar 

  20. Pershin, Y.V., Di Ventra, M.: Memristive circuits simulate memcapacitors and meminductors. Electron. Lett. 46, 517–518 (2010)

    Article  Google Scholar 

  21. Pershin, Y.V., Di Ventra, M.: Emulation of floating memcapacitors and meminductors using current conveyors. Electron. Lett. 47, 243–244 (2011)

    Article  Google Scholar 

  22. Liang, Y., Chen, H., Yu, D.S.: A practical implementation of a floating memristor-less meminductor emulator. IEEE Trans. Circuits Syst. II(61), 299–303 (2014)

    Google Scholar 

  23. Biolek, D., Biolek, Z., Biolková, V.: PSPICE modeling of meminductor. Analog Integr. Circuits Signal Process. 66, 129–137 (2011)

  24. Wang, H., Wang, X., Li, C.D., Chen, L.: SPICE mutator model for transforming memristor into meminductor. Abstr. Appl. Anal. (2013). doi:10.1155/2013/281675

  25. Han, J.H., Song, C., Gao, S., Wang, Y.Y., Chen, C., Pan, F.: Realization of the meminductor. ACS Nano 8, 10043–10047 (2014)

    Article  Google Scholar 

  26. Biolek, D., Biolek, Z., Biolková, V.: Pinched hysteretic loops of ideal memristors, memcapacitors and meminductors must be ‘self-crossing’. Electron. Lett. 47, 1385–1387 (2011)

  27. Yin, Z.Y., Tian, H., Chen, G.H., Chua, L.O.: What are memristor, memcapacitor, and meminductor? IEEE Trans. Circuits Syst. 62, 402–406 (2015)

    Article  Google Scholar 

  28. Yuan, F., Wang, G.Y., Jin, P.P.: Study on dynamical characteristics of a meminductor model and its meminductor-based oscillator. Acta Phys. Sin. 64, 210504 (2015)

    Google Scholar 

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

    Article  Google Scholar 

  30. Xu, B.R.: A simplest parallel chaotic system of memristor. Acta Phys. Sin. 62, 190506 (2013)

    Google Scholar 

  31. Teng, L., Iu, H.H.C., Wang, X.Y., Wang, X.K.: Chaotic behavior in fractional-order memristor-based simplest chaotic circuit using fourth degree polynomial. Nonlinear Dyn. 77, 231–241 (2014)

    Article  Google Scholar 

  32. Chen, M., Li, M.Y., Yu, Q., Bao, B.C., Xu, Q., Wang, J.: Dynamics of self-excited attractors and hidden attractors in generalized memristor based Chua’s circuit. Nonlinear Dyn. 81, 215–226 (2015)

    Article  MathSciNet  Google Scholar 

  33. Yu, Q., Bao, B.C., Xu, Q., Chen, M., Hu, W.: Inductorless chaotic circuit based on active generalized memristors. Acta Phys. Sin. 64, 170503 (2015)

    Google Scholar 

  34. Bao, B.C., Hu, F.W., Chen, M., Xu, Q., Yu, Y.J.: Self-excited and hidden attractors found simultaneously in a modified Chua’s circuit. Int. J. Bifurc. Chaos 25, 1550075 (2015)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61271064, 60971046, 61401134), the Natural Science Foundations of Zhejiang Province (Grant Nos. LZ12F01001, LQ14F010008), the Natural Science Foundations of Fujian Province (Grant No. 2016J01761), and the Program for Zhejiang Leading Team of S&T Innovation (Grant No. 2010R50010).

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Authors and Affiliations

  1. Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou, 310018, China

    Birong Xu, Guangyi Wang & Yiran Shen

  2. College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan, 354300, China

    Birong Xu

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  1. Birong Xu
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  2. Guangyi Wang
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  3. Yiran Shen
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Correspondence to Guangyi Wang.

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Xu, B., Wang, G. & Shen, Y. A simple meminductor-based chaotic system with complicated dynamics. Nonlinear Dyn 88, 2071–2089 (2017). https://doi.org/10.1007/s11071-017-3363-y

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  • DOI: https://doi.org/10.1007/s11071-017-3363-y

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