Abstract
The theory of memristor was postulated in the year of 1971 by Leon O. Chua. The intensive interest on memristive systems is given by the researchers since after the physical realization of the hysteresis behavior in a nanoscale TiO\(_{\mathrm {2}}\) memristor in 2008 by a group of researchers at HP Labs lead by Stanley Williams. Research on memristive systems has been carried out on various capacities such as understanding the mathematics of memristor, finding new materials which have memristive properties, studying the underlying dynamics of memristive systems and revisiting the existing concepts with memristor as a nonlinear element. As a result, memristors have potential applications in various domains. It ranges from neural networks, memory devices, artificial intelligence, high speed computing, nano batteries and human skin modeling, etc. In the recent times, much attention is given to explore the nonlinear dynamics of memristor based circuits. In this chapter, we consider a smooth continuous cubic memristor as nonlinear element. It is applied to (a) an autonomous and (b) a non-autonomous dynamical systems namely, the Chua’s circuit and Duffing Oscillator, to study the associated dynamics of these systems. The numerical simulation of the circuit systems as well as its hardware experimental studies are performed in the laboratory. An inductor free realization and volume expanded period doubling scenario in a memristive Chua’s circuit is studied. The complex behaviors, like, bifurcations and chaos, three-tori, transient chaos and intermittency in a memristive Duffing oscillator are described. In addition, “0–1 test” for the experimental time series data characterizing the regular and chaotic dynamics of the proposed circuits are also discussed.
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References
Banerjee, T. (2012). Single amplifier biquad based inductor-free Chua’s circuit. Nonlinear Dynamics, 68, 565–573.
Bao, B.-C., Xu, J.-P., & Liu, Z. (2010). Initial state dependent dynamical behviours in a memristor based chaotic circuit. Chinese Physics Letters, 27(7), 070504.
Bao, B.-C., Fei, F., Wei, D., & Pan, S.-H. (2013). The voltage-current relationship and equivalent circuit implementation of parallel flux-controlled memristive circuits. Chinese Physics B, 22(6), 068401.
Bharathwaj, M., Blain, T., & Sundqvist, K. (2009). A synthetic inductor implementation of Chua’s circuit. EECS Department, University of California, Berkeley. UCB/EECS-2009-20.
Bleher, S., Grebogi, C., & Ott, E. (1990). Bifurcation to chaotic scattering. Physica D: Nonlinear Phenomena, 46, 87–121.
Botta, V. A., Nespoli, C., & Messias, M. (2011). Mathematical analysis of a third order memristor based Chua’s oscillator. TEMA Tendencias em Matematica Aplicada e Computacional, 12(2), 91–99.
Chua, L. O. (1971). Memristor-the missing circuit element. IEEE Transactions on Circuit Theory, 18, 507–519.
Corinto, F., & Ascoli, A. (2012). Memristive diode bridge with LCR filter. Electronics Letters, 48(14), 824–825.
Dhamala, M., & Lai, Y.-C. (1999). Controlling transient chaos in deterministic flows with applications to electrical power systems and ecology. Physical Review E, 59, 1646.
Fouda, M. E., & Radwan, M. G. (2014). Memristor-based voltage-controlled relaxation oscillators. International Journal of Circuit Theory and Applications, 42, 1092–1102.
George, D. (1918). Erzwungene schwingung bei vernderlicher eigenfrequenz und ihre technische bedeutung. Vieweg.
Gopal, R., Venkatesan, A., & Lakshmanan, M. (2013). Applicability of 0–1 test for strange nonchaotic attractors. Chaos, 23, 023123.
Gottwald, G. A., & Melbourne, I. (2004). A new test for chaos in deterministic systems. Proceedings of the Royal Society of London A, 460, 603–611.
Ishaq Ahamed, I., & Lakshmanan, M. (2013). Nonsmooth bifurcations, transient hyperchaos and hyperchaotic beats in a memristive Murali-Lakshmanan-Chua’s circuit. International Journal of Bifurcation and Chaos, 23(6), 1350098.
Ishaq Ahamed, I., Srinivasan, K., Murali, K., & Lakshmanan, M. (2011). Observation of chaotic beats in a driven memristive Chua’s circuit. International Journal of Bifurcation and Chaos, 21(3), 737–757.
Itoh, M., & Chua, L. O. (2008). Memristor oscillators. International Journal of Bifurcation and Chaos, 18(11), 3183–3206.
Jothimurugan, R., Suresh, K., Ezhilarasu, M., & Thamilmaran, K. (2014). Improved realization of canonical Chua’s circuit with synthetic inductor using current feedback operational amplifiers. AEU—International Journal of Electronics and Communications, 68(5), 413–421.
Jung, C., Tél, T., & Ziemniak, E. (1993). Application of scattering chaos to particle transport in a hydrodynamical flow. Chaos: An Interdisciplinary Journal of Nonlinear Science, 3, 555–568.
Kim, H., Sah, M., Yang, C., Cho, S., & Chua, L. (2012). Memristor emulator for memristor circuit applications. IEEE Transactions on CAS, I(59), 2422–2431.
Kovacic, I., & Brennan, M. J. (2011). The Duffing equation: Nonlinear oscillators and their behaviour. Wiley.
Kulp, C. W., & Smith, S. (2011). Characterization of noisy symbolic time series. Physical Review E, 83, 026201.
Kyriakides, E., & Georgiou, J. (2014). A compact, low-frequency, memristor-based oscillator. International Journal of Circuit Theory and Applications.
Lai, Y.-C., & Tél, T. (2011). Transient chaos: Complex dynamics on finite time scales (Vol. 173). Springer Science & Business Media.
Li, Y., Huang, X., & Guo, M. (2013). The generation, analysis, and circuit implementation of a new memristor based chaotic system. Mathematical Problems in Engineering, 398306.
Li, H., Wang, L., & Duan, S. (2014). A memristor-based scroll chaotic system—design, analysis and circuit implementation. International Journal of Bifurcation and Chaos, 24, 1450099.
Manneville, P., & Pomeau, Y. (1979). Intermittency and the Lorenz model. Physics Letters A, 75, 1–2.
Martinsen, O. G., Grimnes, S., Lütken, C. A., & Johnsen, G. K. (2010). Memristance in human skin. Journal of Physics: Conference Series, 224, 012071.
Morgül, Ö. (1995). Inductorless realization of Chua’s oscillator. Electronics Letters, 31, 1424–1430.
Muthuswamy, B. (2010). Implementing memristor based Chaotic circuits. International Journal of Bifurcation and Chaos, 20(5), 1335–1350.
Sabarathinam, S., & Thamilmaran, K. (2015). Transient chaos in a globally coupled system of nearly conservative Hamiltonian duffing oscillators. Chaos, Solitons & Fractals, 73, 129–140.
Sánchez-Lópeza, C., Carrasco-Aguilara, M., & Muñiz-Montero, C. (2015). A 16 Hz-160 kHz memristor emulator circuit. International Journal of Electronics and Communications (AEU), 69, 1208–1219.
Secco, J., Biey, M., Corinto, F., Ascoli, A., & Tetzlaff, R. (2015). Complex behavior in memristor circuits based on static nonlinear two-ports and dynamic bipole. IEEE—European Conference on Circuit Theory and Design (ECCTD), 1–4.
Slipko, V. A., Pershin, Y. V., & Di Ventra, M. (2013). Changing the state of a memristive system with white noise. Physical Review E, 87, 042103.
Strukov, D. B., Snider, G. S., Stewart, D. R., & Stanley Williams, R. (2008). The missing memristor found. Nature, 453, 80–83.
Tél, T., & Lai, Y.-C. (2008). Chaotic transients in spatially extended systems. Physics Reports, 460, 245–275.
Teng, L., Iu, H. H. C., Wang, X., & Wang, X. (2014). Chaotic behavior in fractionalorder memristor-based simplest chaotic circuit using fourth degree polynomial. Nonlinear Dynamics, 77, 231–241.
Thomas, A. (2013). Memristor-based neural networks. Journal of Physics D: Applied Physics, 46, 093001.
Tôrres, L., & Aguirre, L. (2000). Inductorless Chua’s circuit. Electronics Letters, 36, 1915–1916.
Valov, I., Linn, E., Tappertzhofen, S., Schmelzer, S., van den Hurk, J., Lentz, F., et al. (2013). Nanobatteries in redox-based resistive switches require extension of memristor theory. Nature Communications, 4, 1771.
Valsa, J., Biolek, D., & Biolek, Z. (2011). An analogue model of the memristor. International Journal of Numerical Modelling, 24, 400–408.
Yang, J. J., Pickett, M. D., Li, X., Ohlberg, D. A. A., Stewart, D. R., & Stanley Williams, R. (2008). Memristive switching mechanism for metal/oxide/metal nanodevices. Nature Nanotechnology, 3, 429–433.
Zakhidov, A. A., Jung, B., Slinker, J. D., Abruña, H. D., & Malliaras, G. G. (2010). A light-emitting memristor. Organic Electronics, 11, 150–153.
Zidan, M. A., Omran, H., Smith, C., Syed, A., Radwan, A. G., & Salama, K. N. (2014). A family of memristorbased reactance-less oscillators. International Journal of Circuit Theory and Applications, 42, 1103–1122.
Acknowledgements
R.J and S.S knowledges the financial support of University Grants Commission, India through UGC (BSR)-RFSMS scheme. K.S is thankful to the financial support of the Department of Science and Technology (DST), India through PURSE scheme. K.T is grateful to DST, India for the financial support in form of major research project.
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Jothimurugan, R., Sabarathinam, S., Suresh, K., Thamilmaran, K. (2017). Experimental Analogue Implementation of Memristor Based Chaotic Oscillators. In: Vaidyanathan, S., Volos, C. (eds) Advances in Memristors, Memristive Devices and Systems. Studies in Computational Intelligence, vol 701. Springer, Cham. https://doi.org/10.1007/978-3-319-51724-7_14
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