Model of Bernoulli Memristors in the Form of Split Signals Polynomial

In the paper, the behavioral model of a memristor, in which the current dynamics is described by the differential Bernoulli equation, is represented. as a polynomial of split signals. On exciting by a harmonic signal, the behavioral model is built as the two-dimensional polynomial of split signals for a transfer characteristic of the Bernoulli memristor. The splitting of the input signals provides the uniqueness of the input-output mapping, the model adaptation to the specified class of the input signals and, therefore, the model simplicity compared to general nonlinear models, for example, the Volterra series and neural networks. The harmonic input signal is splitted by means of the delay line. It is shown that the vector signal containing the input signal and its delay in time by one step is split and has the smallest possible length according to the splitting conditions. The two-dimensional polynomial of the third power, built on the elements of the vector signal, provides high precision modeling of the transfer characteristic of the Bernoulli memristor in the mean-squared norm.

Keywords

memristor; nonlinear dynamic system; behavioral model; multidimensional polynomial.

References

1. Abunahla H., Mohammad B. Memristor Technology: Synthesis and Modeling for Sensing and Security Applications. Cham, Springer, 2018.
2. Vourkas I., Sirkoulis G.Ch. Memristor-Based Nanoelectronic Computing Circuits and Architectures. Cham, Springer, 2016.
3. Radwan A.G., Fouda M.E. On the Mathematical Modeling of Memristor, Memcapacitor and Meminductor. Cham, Springer, 2015.
4. Solovyeva E.B. Operator Approach to Nonlinear Compensator Synthesis for Communication Systems. International Siberian Conference on Control and Communications, Moscow, 2016, pp. 1-5. DOI: 10.1109/SIBCON.2016.7491653
5. Solovyeva E.B. A Split Signal Polynomial as a Model of an Impulse Noise Filter for Speech Signal Recovery. Journal of Physics: Conference Series. International Conference on Information Technologies in Business and Industry, 2017, vol. 803, no. 1. pp. 1-6. DOI: 10.1088/1742-6596/803/1/012156
6. Biolek Z., Biolek D., Biolkova V. Differential Equations of Ideal Memristors. Radioengineering, 2015, vol. 24, no. 2, pp. 369-377. DOI: 10.13164/re.2015.0369
7. Chao Ma, Shuguo Xie, Yunfeng Jia, Guanyu Lin. Macromodeling of the Memristor Using Piecewise Volterra Series. Microelectronics Journal, 2014, vol. 45, no. 3, pp. 325-329. DOI: 10.1016/j.mejo.2013.11.017
8. Georgiou P.S., Barahona M., Yaliraki S.N., Drakakis E.M. Device Properties of Bernoulli Memristors. Proceedings of the IEEE, 2012, vol. 100, no. 6, pp. 1938-1950. DOI: 10.1109/JPROC.2011.2164889