Abstract
The simplest chaotic circuit containing a memristor involves a capacitor C, an inductor L, and two parameters, α and β, characterizing the memristor. Chaos was observed experimentally for three combinations of these parameters. Here, we report high resolution stability diagrams displaying an abundance of tunable ranges of periodic and chaotic self-oscillations for this circuit, in all six possible control planes. We predict dynamically rich and intricate sequences of oscillations that are experimentally accessible in the system.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Muthuswamy, L.O. Chua, Int. J. Bifurc. Chaos 20, 1567 (2010)
S. Vaidyanathan, C. Volos, Advances in memristors, memristive devices and systems (Springer, Cham, 2017)
A.G. Radwan, M.E. Fouda, On the mathematical modeling of memristor, memcapacitor, and meminductor (Springer, Cham, 2015)
A. Adamatzky, L. Chua, Memristor networks (Springer, Cham, 2014)
S. Kumar, J.P. Strachan, R.S. Williams, Nature 548, 318 (2017)
S. Kumar, N. Davila, Z. Wang, X. Huang, J.P. Strachan, D. Vine, A.L.D. Kilcoyne, Y. Nishi, R.S. Williams, Nanoscale 9, 1793 (2017)
G. Wang, M. Cui, B. Cai, X. Wang, T. Hu, Math. Prob. Eng. 2015, 561901 (2015)
A. Ascoli, S. Slesazeck, H. Mahne, R. Tetzlaff, T. Mikolajick, IEEE Trans. Circuits Syst. 62, 1165 (2015)
L. Chua, Nanotechnology 24, 383001 (2013)
T. Driscoll, Y.V. Pershin, D.N. Basov, M. di Ventra, Appl. Phys. A 102, 885 (2011)
J.M. Ginoux, R. Meucci, S. Euzzor, A. di Garbo, Int. J. Bifurc. Chaos 28, 1850128 (2018)
J.M. Ginoux, C. Letellier, L.O. Chua, Int. J. Bifurc. Chaos 20, 3819 (2010)
C. Bonatto, J.A.C. Gallas, Phys. Rev. Lett. 101, 054101 (2008)
J.A.C. Gallas, Int. J. Bifurc. Chaos 20, 197 (2010)
R. Vitolo, P. Glendinning, J.A.C. Gallas, Phys. Rev. E 84, 016216 (2011)
J.A.C. Gallas, Adv. At. Mol. Opt. Phys. 65, 127 (2016)
G.M. Ramírez-Ávila, J.A.C. Gallas, Phys. Lett. A 375, 143 (2010)
Y. Zhang, X. Zhang, Int. J. Bifurc. Chaos 23, 1350136 (2013)
J. Llibre, C. Valls, J. Nonlinear Math. Phys. 19, 1250029 (2012)
F. Yuan, G. Wang, X. Wang, Chaos 27, 033103 (2017)
H. Wu, B. Bao, Z. Liu, Q. Xu, P. Jiang, Nonlinear Dyn. 83, 893 (2016)
L.V. Gambuzza, L. Fortuna, M. Frasca, E. Gale, Int. J. Bifurc. Chaos 25, 1550101 (2015)
A. Buscarino, L. Fortuna, M. Frasca, L.V. Gambuzza, Int. J. Bifurc. Chaos 23, 1330015 (2013)
B. Muthuswamy, Int. J. Bifurc. Chaos 20, 1353 (2010)
J.G. Freire, J.A.C. Gallas, Phys. Chem. Chem. Phys. 13, 12191 (2011)
J.A.C. Gallas, Phys. Rev. Lett. 70, 2714 (1993)
E.N. Lorenz, Physica D 237, 1689 (2008)
W. Façanha, B. Oldeman, L. Glass, Phys. Lett. A 377, 1264 (2013)
R.E. Francke, T. Pöschel, J.A.C. Gallas, Phys. Rev. E 87, 042907 (2013)
L. Junges, J.A.C. Gallas, Phys. Lett. A 376, 2109 (2012)
J. Bragard, H. Pleiner, O.J. Suarez, P. Vargas, J.A.C. Gallas, D. Laroze, Phys. Rev. E 84, 037202 (2011)
M.R. Gallas, M.R. Gallas, J.A.C. Gallas, Eur. Phys. J. Special Topics 223, 2131 (2014)
A. Sack, J.G. Freire, E. Lindberg, T. Pöschel, J.A.C. Gallas, Sci. Rep. 3, 3350 (2013)
F.F.G. Sousa, R.M. Rubinger, J.C. Sartorelli, H.A. Albuquerque, M.S. Baptista, Chaos 26, 083107 (2016)
D.W.C. Marcondes, G.F. Comassetto, B.G. Pedro, J.C.C. Vieira, A. Hoff, F. Prebianca, C. Manchein, H.A. Albuquerque, Int. J. Bifurc. Chaos 27, 1750175 (2017)
C. Manchein, H.A. Albuquerque, L.F. Mello, Int. J. Bifurc. Chaos 28, 1830038 (2018)
Acknowledgments
Open Access funding provided by Max-Planck Society.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Gallas, J.A.C. Stability diagrams for a memristor oscillator. Eur. Phys. J. Spec. Top. 228, 2081–2091 (2019). https://doi.org/10.1140/epjst/e2019-900009-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2019-900009-8