IEEE Circuits and Systems Magazine - Q2 2018 - 27

VI. Conclusion
In this paper a novel generic memristor, dubbed the 4-lobe
Chua corsage memristor, is proposed on the basis of the
Chua corsage memristor. We designed an oscillator circuit by connecting an external inductor in series with the
4-lobe Chua corsage memristor and a battery. The oscillation generated by the oscillator circuit is verified with an
in depth analysis from nonlinear dynamics, via local activity, edge of chaos, and the Hopf bifurcation theorem.
The small-signal equivalent circuit of the 4-lobe
Chua corsage memristor is determined by operating
the device at an equilibrium point chosen on the negative slope of the DC V-I curve. The oscillating frequency
~ ) is obtained using the condition of Re Z (i~ ) ) = 0
for the same equilibrium point whereas the external inductor L) value is calculated from the equation
L) = 1/ (~ ) # Im Y (i~ ))).
By exploiting local activity, and applying the edge of
chaos theorem we proved that the 4-lobe Chua corsage
memristor is locally active and contains an edge of chaos domain over the input voltage range - 9 V < V < - 3 V.
Due to the local activity and the edge of chaos regime,
when the first-order locally-active 4-lobe Chua corsage
memristor is connected in series with a positive inductance L, and a battery, the resulting circuit exhibits a
super critical Hopf bifurcation, resulting in a stable smallsinusoidal oscillation.
Zubaer Ibna Mannan received his B.S.
and M.S. degrees in electrical and electronics engineering, and electronics and information engineering from East West
University, Bangladesh and Chonbuk National University, Republic of Korea in
2010 and 2016, respectively. Currently, he is pursuing his
Ph.D. degree in electronics and information engineering
at Chonbuk National University and working as a researcher in the Intelligent Robots Research Center (IRRC).
His research interests include circuit design of memristor based bioelectronics devices, hardware implementation of cellular neural/nonlinear network, and
designing of memristive oscillator based on bifurcation
and chaos theory.
Changju Yang was born in Jeon-ju, Korea, on 1981. He received the B.S., M.S.,
and Ph.D. degrees in electronics and information engineering from Chonbuk National University, Korea, in 2008, 2010,
and 2014, respectively. He is currently
working as a Post-Doctoral in the Division of Electronics

sEcOnd quartEr 2018

and Information Engineering in Chonbuk National University, Korea and as a research fellow in Intelligent Robots Research Center (IRRC).
His research interests include memristor emulator application, artificial intelligence, cellular neural networks,
CMOS based circuit design for learning algorithm, analysis of memristor and memristive system.
Hyongsuk Kim (Senior Member, IEEE)
received the Ph.D. degree in electrical
engineering from the University of Missouri, Columbia, in 1992.
Since 1993, he has been a Professor
with the Division of Electronics Engineering, Chonbuk National University, Jeonju, Korea.
From 2000 to 2002 and again from 2009 to 2010, he was
with the Nonlinear Electronics Laboratory, Electrical
Engineering and Computer Science (EECS) Department,
University of California at Berkeley, Berkeley, as a Visiting Scholar. His current research interests include
memristors and its application to the implementation of
neural networks.
References
[1] V. K. Mehta and R. Mehta, "Sinusoidal oscillators," in Principles of
Electronics, 11th ed. India: S. Chand & Co, 2005, ch, 14, sec. 3-4, pp.
366-368.
[2] M. P. Sah, Z. I. Mannan, H. Kim, and L. Chua, "Oscillator made of only
one memristor and one battery," Int. J. Bifurcation Chaos, vol. 25, no. 3,
pp. 150001-15000-28, Mar. 2015.
[3] Z. I. Mannan, H. Choi, and H. Kim, "Chua corsage memristor oscillator via Hopf bifurcation," Int. J. Bifurcation Chaos, vol. 26, no. 3, pp.
1630009-1-1630028, Apr. 2016.
[4] L. Chua, "If it's pinched it's a memristor," Semicond. Sci. Technol., vol.
29, no. 10, pp. 104001-1-104042, Sept. 2014.
[5] L. O. Chua, Introduction to Nonlinear Network Theory. New York:
McGraw-Hill, 1969.
[6] L. O. Chua, C. A. Desoer, and E. S. Kuh, Linear and Nonlinear Circuits.
New York: McGraw-Hill, 1987.
[7] L. O. Chua and T. Roska, Cellular Neural Networks and Visual Computing: Foundations and Applications. New York: Cambridge Univ. Press,
2002.
[8] L. Chua, "Everything you wish to know about memristors but are
afraid to ask," Radioengineering, vol. 24, no. 2, pp. 319-368, June 2015.
[9] Z. I. Mannan, H. Cheol, V. Rajamani, H. Kim, and L. Chua, "Chua corsage memristor: Phase portraits, basin of attraction, and coexisting
pinched hysteresis loops," Int. J. Bifurcation Chaos, vol. 27, no. 3, pp.
173001-1-173036, Mar. 2017.
[10] L. O. Chua and S. M. Kang, "Memristive devices and systems," Proc.
IEEE, vol. 64, no. 2, pp. 209-223, Feb. 1976.
[11] K. Mainzer and L. Chua, Local Activity Principle: The Cause of Complexity and Symmetry Breaking, London, U.K.: Imperial College Press,
2013.
[12] R. Dogaru and L. O. Chua, "Edge of chaos and local activity domain
of FitzHugh-Nagumo equation," Int. J. Bifurcation Chaos, vol. 8, no. 2,
pp. 211-257, Feb. 1998.
[13] Yu. A. Kuznetsov. (2006) Andronov: Hopf bifurcation SCHOLARPEDIA.
[Online]. Available: http://www.scholarpedia.org/article/AndronovHopf_bifurcation
[14] S. H. Strogatz, Nonlinear Dynamics and Chaos, 2nd ed. Reading, MA:
Addison-Wesley, 1994.

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