×

Dynamic analysis of a bistable bi-local active memristor and its associated oscillator system. (English) Zbl 1397.34076

Summary: This paper proposes a new type of memristor with two distinct stable pinched hysteresis loops and twin symmetrical local activity domains, named as a bistable bi-local active memristor. A detailed and comprehensive analysis of the memristor and its associated oscillator system is carried out to verify its dynamic behaviors based on nonlinear circuit theory and Hopf bifurcation theory. The local-activity domains and the edge-of-chaos domains of the memristor, which are both symmetric with respect to the origin, are confirmed by utilizing the mathematical cogent theory. Finally, the subcritical Hopf bifurcation phenomenon is identified in the subcritical Hopf bifurcation region of the memristor.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
94C05 Analytic circuit theory
34C28 Complex behavior and chaotic systems of ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C55 Hysteresis for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adhikari, S. P.; Sah, M. P.; Kim, H.; Chua, L. O., Three fingerprints of memristor, IEEE Trans. Circuits Syst.-I, 60, 3008-3021, (2013)
[2] Ascoli, A.; Tetzlaff, R.; Chua, L. O., The first ever real bistable memristors — part I: theoretical insights on local fading memory, IEEE Trans. Circuits Syst.-II, 63, 1091-1095, (2016)
[3] Chua, L. O., Memristors — the missing circuit element, IEEE Trans. Circuit Th., CT-18, 507-519, (1971)
[4] Chua, L. O.; Kang, S. M., Memristive devices and systems, Proc. IEEE, 64, 209-223, (1976)
[5] Chua, L. O.; Desoer, C. A.; Kuh, E. S., Linear and Nonlinear Circuits, (1987), McGraw-Hill · Zbl 0631.94017
[6] Chua, L. O.; Sbitnev, V.; Kim, H., Hodgkin-Huxley axon is made of memristor, Int. J. Bifurcation and Chaos, 22, 1230011-1-48, (2012) · Zbl 1270.94073
[7] Chua, L. O.; Sbitnev, V.; Kim, H., Neurons are poised near the edge of chaos, Int. J. Bifurcation and Chaos, 22, 1250098-1-49, (2012)
[8] Chua, L. O., If it’s pinched it’s a memristor, Semicond. Sci. Technol., 29, 104001-1-42, (2014)
[9] Chua, L. O., Everything you wish to know about memristor but are afraid to ask, Radioengin., 24, 319-368, (2015)
[10] Dodaru, R.; Chua, L. O., Edge of chaos and local activity domain of Fitzhugh-Nagumo equation, Int. J. Bifurcation and Chaos, 8, 211-257, (1998) · Zbl 0933.37042
[11] Dou, G.; Yu, Y.; Guo, M.; Zhang, Y.; Sun, Z.; Li, Y., Memristive behavior based on ba-doped srtio_{3} films, Chin. Phys. Lett., 34, 038502-1-4, (2017)
[12] Eshraghian, K.; Cho, K.; Kavehei, O.; Kang, O.; Abbott, D.; Kang, S. S., Memristor MOS content addressable memory (MCAM): hybrid architecture for future high performance search engines, IEEE Trans. VLSI Syst., 19, 1407-1417, (2011)
[13] Guo, M.; Xue, Y.; Gao, Z.; Zhang, Y.; Dou, G.; Li, Y., Dynamic analysis of a physical SBT memristor-based chaotic circuit, Int. J. Bifurcation and Chaos, 27, 1730047-1-13, (2017) · Zbl 1420.94119
[14] Hagiwara, S.; Hayashi, H.; Takahashi, K., Calcium and potassium currents of the membrane of a barnacle muscle fibre in relation to the calcium spike, J. Physiol., 205, 115-129, (1969)
[15] Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117, 500-544, (1952)
[16] Huang, X.; Jia, J.; Li, Y.; Wang, Z., Complex nonlinear dynamics in fractional and integer order memristor-based systems, Neurocomputing, 218, 296-306, (2016)
[17] Huang, X.; Fan, Y.; Jia, J.; Wang, Z.; Li, Y., Quasi-synchronization of fractional-order memristor-based neural networks with parameter mismatches, IET Contr. Th. Appl., 11, 2317-2327, (2017)
[18] Joglekar, Y. N.; Wolf, S. J., The elusive memristor: properties of basic electrical circuits, Eur. J. Phys., 30, 661-675, (2009) · Zbl 1173.78314
[19] Li, Y.; Dou, G., Towards the implementation of memristor: A study of the electric properties of ba\({}_{0 . 7 7}\)sr\({}_{0 . 2 3}\)tio_{3} material, Int. J. Bifurcation and Chaos, 23, 1350204-1-6, (2013)
[20] Li, Y.; Huang, X.; Song, Y.; Lin, J., A new fourth-order memristive chaotic system and its generation, Int. J. Bifurcation and Chaos, 25, 1550151-1-9, (2015)
[21] Mainzer, K.; Chua, L. O., Local Activity Principle: The Cause of Complexity and Symmetry Breaking, (2013), Imperial College Press
[22] Mannan, Z. I.; Choi, H.; Kim, H., Chua corsage memristor oscillator via Hopf bifurcation, Int. J. Bifurcation and Chaos, 25, 1530010-1-28, (2016) · Zbl 1338.34095
[23] Mannan, Z. I.; Choi, H.; Kim, H.; Chua, L. O., Chua corsage memristor: phase portraits, basin of attraction, and coexisting pinched hysteresis loops, Int. J. Bifurcation and Chaos, 27, 1730011-1-36, (2017) · Zbl 1360.34110
[24] Rajamani, V.; Sah, M. P.; Mannan, Z.; Kim, H.; Chua, L. O., Third-order memristor Morris-lecar model of barnacle muscle fiber, Int. J. Bifurcation and Chaos, 27, 1730015-1-58, (2017) · Zbl 1366.34068
[25] Sah, M. P.; Eroglu, A.; Chua, L. O., Memristive model of the barnacle giant muscle fibers, Int. J. Bifurcation and Chaos, 26, 1630001-1-40, (2016) · Zbl 1334.34106
[26] Strukov, D. B.; Snider, G. S.; Stewart, G. R.; Williams, R. S., The missing memristor found, Nature, 453, 80-83, (2008)
[27] Wen, S.; Zeng, Z.; Huang, T.; Chen, Y., Passivity analysis of memristor-based recurrent neural networks with time-varying delays, J. Franklin Inst., 350, 2354-2370, (2013) · Zbl 1293.93095
[28] Yao, J.; Sun, Z. Z.; Zhong, L.; Natelson, D.; Tour, J. M., Resistive switches and memories from silicon oxide, Nano Lett., 10, 4105-4110, (2010)
[29] Zhang, Y.; Dou, G.; Sun, Z.; Guo, M.; Li, Y., Establishment of physical and mathematical models for sr\({}_{0 . 9 5}\)ba\({}_{0 . 0 5}\)tio_{3} memristor, Int. J. Bifurcation and Chaos, 27, 1750148-1-10, (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.