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Dynamics of Delayed Memristive Systems in Combination Chaotic Circuits

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Book cover Advances in Memristors, Memristive Devices and Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 701))

Abstract

The use of memristor in the realization of chaotic circuits has gained popularity in recent times. This can be attributed to its simplicity over the traditional Chua’s diode. The memristor as a nanometer-scale passive circuit element which can be described as a resistor with memory and possesses nonlinear characteristics. In this chapter, the numerical and experimental dynamics of non-autonomous time delay memristive oscillator which consists of negative conductance and smooth-cubic memristor are reported. Diffusive and negative feed back coupling of combination-combination arrays of the electronic circuits are also presented. The viability of both numerical and electronic simulation are also presented.

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References

  • Adelakun, A. O. (2013). Solutions of semistate duffing van der pol and bonhoeffer van der pol electronic circuits with memristor. Journal of Nigerian Association of Mathematical Physics, 25(2).

    Google Scholar 

  • Adelakun, A. O. (2014). Purely imaginary eigenvalues (pie) in extended circuits with mem-devices. Journal of Electrical and Electronics Engineering, 9(3), 1–8.

    Google Scholar 

  • Adelakun, A. O., Adeiza, O. F., & Oketayo, O. (2014a). Unidirectional synchronization of two identical jerk oscillators with memristor. Journal of Nigerian Association of Mathematical Physics, 28(2), 35–42.

    Google Scholar 

  • Adelakun, A. O., Egunjobi, I. A., & Oketayo, O. (2014b). Synchronization of new jerk oscillator and it’s application to secure communication. Journal of Nigerian Association of Mathematical Physics, 28(2), 27–34.

    Google Scholar 

  • Aihara, K. (1991). Chaotic dynamics in nerve membranes and its modelling with an artificial neuron. In IEEE international sympoisum on circuits and systems, 1991 (Vol. 3, pp. 1457–1460). doi:10.1109/ISCAS.1991.176649.

  • Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., et al. (2005). Chaos-based communications at high bit rates using commercial fibre-optic links. Nature, 438(7066), 343–346. doi:10.1038/nature04275.

  • Azar, A. T., & Vaidyanathan, S. (2016). Advances in Chaos Theory and Intelligent Control. Berlin, Germany: Springer.

    Book  MATH  Google Scholar 

  • Bo-Cheng, B., Jian-Ping, X., Guo-Hua, Z., Zheng-Hua, M., & Ling, Z. (2011). Chaotic memristive circuit: Equivalent circuit realization and dynamical analysis. Chinese Physics B, 20(12), 120502.

    Google Scholar 

  • Boccaletti, S., Kurths, J., Osipov, G., Valladares, D., & Zhou, C. S. (2002). The synchronization of chaotic systems. Physics Reports, 366, 1–101.

    Article  MathSciNet  MATH  Google Scholar 

  • Chua, L. O. (1971). Memristor the missing circuit element. IEEE Transactions on Circuit Theory, 18, 507–519.

    Google Scholar 

  • Chua, L. O., Komuro, M., & Matsumoto, T. (1986). The double scroll family, part I and II. IEEE Transaction in Circuit and System, CAS-33, 1073–1118.

    Google Scholar 

  • El-Sayed, A., Elsaid, A., Nour, H., & Elsonbaty, A. (2013). Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit. Communications in Nonlinear Science and Numerical Simulation, 18(1), 148–170. doi:10.1016/j.cnsns.2012.06.011.

    Article  MathSciNet  MATH  Google Scholar 

  • El-Sayed, A., Nour, H., Elsaid, A., Matouk, A., & Elsonbaty, A. (2016). Dynamical behaviors, circuit realization, chaos control, and synchronization of a new fractional order hyperchaotic system. Applied Mathematical Modelling, 40(5), 3516–3534. doi:10.1016/j.apm.2015.10.010.

    Article  MathSciNet  Google Scholar 

  • Elhadj, Z., & Sprott, J. C. (2008). On the robustness of chaos in dynamical systems: Theories and applications. Frontiers of Physics in China, 3, 195. doi:10.1007/s11467-008-0017-z.

    Article  Google Scholar 

  • Fuwape, I. A., & Ogunjo, S. T. (2015). Fractal and entropy analysis of nigerian all share index (ASI) and gross domestic product (GDP). In 2nd international conference and exhibition (OWSD-FUTA) (pp. 330–333).

    Google Scholar 

  • Fuwape, I. A., Ogunjo, S. T., Oluyamo, S. S., & Rabiu, A. B. (2016). Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria. Theoretical and Applied Climatology. doi:10.1007/s00704-016-1867-x.

  • Fuwape, I. I. A., & Ogunjo, S. T. (2013). Investigating Chaos in the Nigerian Asset and Resource Management (ARM) Discovery Fund. CBN Journal of Applied Statistics, 4(2), 129–140.

    Google Scholar 

  • Itoh, M., & Chua, L. O. (2008). Memristor oscillators. Interntional Journal of Bifurcation and Chaos, 18(11), 3183–3206.

    Article  MathSciNet  MATH  Google Scholar 

  • Jinfeng, H., & Jingbo, G. (2008). Breaking a chaotic secure communication scheme. Chaos, 18(013), 121. doi:10.1063/1.2885388.

    MathSciNet  MATH  Google Scholar 

  • Li, S., Álvarez, G., Chen, G., & Mou, X. (2012). Breaking a chaos-noise-based secure communication scheme. Chaos, 15(013), 703. doi:10.1063/1.1856711.

    Google Scholar 

  • Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), 130–141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

    Article  Google Scholar 

  • Mamat, M., Salleh, Z., Sanjaya, M. W. S., Noor, N. M. M., & Ahmad, M. F. (2012). Numerical simulation of unidirectional chaotic synchronization of non-autonomous circuit and its application for secure communication. Advanced Studies in Theoretical Physics, 6(10), 497–509.

    MATH  Google Scholar 

  • Mengue, A. D., & Essimbi, B. Z. (2012). Secure communication using chaotic synchronization in mutually coupled semiconductor lasers. Nonlinear Dynamics, 70, 1241–1253. doi:10.1007/s11071-012-0528-6.

    Article  MathSciNet  MATH  Google Scholar 

  • Messias, M., Nespoli, C., & Botta, V. A. (2010). Hopf bifurcation from lines of equilibria without parameters in memristor oscillators. Interntional Journal of Bifurcation and Chaos, 20(2), 437–450.

    Article  MathSciNet  MATH  Google Scholar 

  • Nagaraj, N., & Vaidya, P. G. (2009). Multiplexing of discrete chaotic signals in presence of noise. Chaos, 19(033), 102. doi:10.1063/1.3157183.

    MATH  Google Scholar 

  • Ogunjo, S. T. (2013). Increased and Reduced Order Synchronization of 2D and 3D Dynamical Systems. International Journal of Nonlinear Science, 16(2), 105–112.

    MathSciNet  Google Scholar 

  • Ogunjo, S. T., Fuwape, I. A., & Olufemi, O. I. (2013). Chaotic Dynamics in a Population of Tribolium. FUTA Journal of Research in Sciences, 9(2), 186–193.

    Google Scholar 

  • Ogunjo, S. T., Ojo, K. S., & Fuwape, I. A. (2017). Fractional order control and synchronization of chaotic systems: Studies in computational intelligence. Germany: Springer. chap Comparison of Three Different Synchronization Scheme for Fractional Chaotic Systems.

    Google Scholar 

  • Ojo, K. S., & Ogunjo, S. T. (2012). Synchronization of 4D Rabinovich Hyperchaotic System for Secure Communication. Journal of Nigerian Association of Mathematical Physics, 21, 35–40.

    Google Scholar 

  • Ojo, K. S., Njah, A., & Ogunjo, S. T. (2013). Comparison of backstepping and modified active control in projective synchronization of chaos in an extended Bonhoffer van der Pol oscillator. Pramana, 80(5), 825–835. http://link.springer.com/article/10.1007/s12043-013-0526-3.

  • Ojo, K., Njah, A., Ogunjo, S., & Olusola, O. (2014a). Reduced order hybrid function projective combination synchronization of three Josephson junctions. Archives of Control. http://www.degruyter.com/view/j/acsc.2014.24.issue-1/acsc-2014-0007/acsc-2014-0007.xml.

  • Ojo, K. S., Njah, A., Ogunjo, S. T., & Olusola, O. I. (2014b). Reduced order function projective combination synchronization of three Josephson junctions using backstepping technique. Nonlinear Dynamics and System Theory, 14(2), 119.

    Google Scholar 

  • Ojo, K., Njah, A., & Olusola, O. (2015a). Compound-combination synchronization of chaos in identical and different orders chaotic systems. Archives of Control Sciences, 25(4), 463–490.

    Google Scholar 

  • Ojo, K., Njah, A., & Olusola, O. (2015b). Generalized function projective combination-combination synchronization of chaos in third order chaotic systems. Chinese Journal of Physics, 53(3), l1–16.

    Google Scholar 

  • Ojo, K., Njah, A., & Olusola, O. (2016). Generalized compound synchronization of chaos in different orders chaotic josephson junctions. International Journal of Dynamics and Control, 4(1), 31–39.

    Article  MathSciNet  MATH  Google Scholar 

  • Papadopoulou, M. S., Kyprianidis, I. M., & Stouboulos, I. N. (2008). Complex chaotic dynamics of the double-bell attractor. WSEAS Transactions on Circuits and Systems, 7(1), 13–21.

    Google Scholar 

  • Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64, 821.

    Article  MathSciNet  MATH  Google Scholar 

  • Pehlivan, I., & Uyaroglu, Y. (2010). A new chaotic attractor from general Lorenz system family and its electronic experimental implementation. Turkish Journal of Electrical Engineering and Computer Sciences, 18(2), 171–184. doi:10.3906/elk-0906-67.

    Google Scholar 

  • Shin, S., Sacchetto, D., Leblebici, Y., & Kang, S. M. S. (2012). Neuronal spike event generation by memristors. In 2012 13th international workshop on cellular nanoscale networks and their applications (pp. 1–4). doi:10.1109/CNNA.2012.6331427.

  • Strukov, D., Snider, G., Stewart, D., & Williams, R. (2008). The missing memristor found. Nature, 453, 80–83.

    Article  Google Scholar 

  • Vaidyanathan, S., Volos, C. (2016a). Advances and Applications in Chaotic Systems. Berlin, Germany: Springer.

    Google Scholar 

  • Vaidyanathan S, Volos C (2016b) Advances and Applications in Nonlinear Control Systems. Berlin, Germany: Springer.

    Google Scholar 

  • Wang, H., Wang, Q., & Lu, Q. (2011). Bursting oscillations, bifurcation and synchronization neuronal systems. Chaos, Solitons and Fractals, 44, 667–675.

    Article  MATH  Google Scholar 

  • Wang, Z., Cang, S., Ochola, E. O., & Sun, Y. (2012). A hyperchaotic system without equilibrium. Nonlinear Dynamics, 69(1–2), 531–537. doi:10.1007/s11071-011-0284-z.

    Article  MathSciNet  Google Scholar 

  • Xu, Q., Lin, Y., Bao, B., & Chen, M. (2016). Multiple attractors in a non-ideal active voltage-controlled memristor based chua’s circuit. Chaos, Solitons and Fractals, 83, 186–200.

    Article  MathSciNet  MATH  Google Scholar 

  • Zuo, C., & Cao, H. (2015). One of signatures of a memristor. Communications in Nonlinear Science and Numerical Simulation, 30, 128–138.

    Article  MathSciNet  Google Scholar 

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Correspondence to S. T. Ogunjo .

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Adelakun, O.A., Ogunjo, S.T., Fuwape, I.A. (2017). Dynamics of Delayed Memristive Systems in Combination Chaotic Circuits. 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_19

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  • DOI: https://doi.org/10.1007/978-3-319-51724-7_19

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