IEEE Circuits and Systems Magazine - Q2 2018 - 11

F ^x h = /a k x + b k x - x k + c k sgn ^x - x kh

(1)

This equation has become useful for synthesis of
nonlinear characteristics. Another main topic was related to Leon's discovery of memristor M [3] as the twoterminal fourth basic circuit element after R, L, and C.
While memristors are characterized as
U = f ^q h or q = g (U)

Capacitor
dq = C dv
Memristor
dΦ = M dq

Resistor
dv = R di

(2)

where q and U are integrals of i and v respectively,
thus with memory effect. Leon coined the term memory
resistor (in short memristor). Nearly 150 years after the
definition of inductor in 1831 (resistor in 1827, capacitor
in 1745), memristor was claimed as the fourth basic element with circuit-theoretic justification. In his graduate
course Leon identified the U - q relationship as a hidden
link in a tetrahedron of four electrical variables: v, i, U,
and q. A clear illustration as shown in Fig. 1 shows the
full-fledged identity of memristor.
The concept of memristor was extended to include
various devices such as fluorescent lamps, thermistors, and ionic channels in the membrane wall [4]. Leon
taught a series of graduate courses EE223A, EE223B on
Foundations of Network Theory, and EE225 on Nonlinear Networks for Fall, Winter and Spring quarters at
that time. Also Leon was engaged in authoring a book,
"Computer-Aided Analysis of Electronic Circuits," in
collaboration with Prof. Pen-Min Lin of Purdue University [5]. In this book various algorithms for numerical
solution of nonlinear differential equations describing
electronic circuits were described along with rigorous
analysis of errors. I had an opportunity to proofread
and learn greatly from the draft. In the summer of 1975
I left Berkeley to be an assistant professor at Rutgers
University. After joining Bell Labs in 1977 I taught a graduate course on computer-aided analysis of electronic
circuits in the evening using the Chua and Lin's book.
A memorable episode was to have arrived at the class
completely forgetting to bring my lecture notes, but
managed to teach the class for 90 minutes from sheer
memory of the book materials, thanks to the experience
of proofreading the book while in Berkeley. On June 26
1996 in celebration of Leon's 60th birthday in Seville,
Spain, three conferences were held- The Fourth International Workshop on Cellular Neural Networks and
Their Applications (CNNA-96), International Workshop
on Visions of Nonlinear Science in the 21st Century,
and The Sixth International Specialist Workshop on
Nonlinear Dynamics in Electronic Systems (NDES'96).
Dr. K. K. Phua, chairman of World Scientific Publishing Co.,
edited a specia l volume - A D SE X AG I N TA A N NOS
PROSPERE CELEBRANDOS Celebrating Six Decades of
sEcOnd quartEr 2018

Charge
q

Voltage
v

dΦ

t
id

Inductor
dΦ = L di

vd
t

Flux
Φ

Current
i
Figure 1. constitutive relationship of memristor.

Figure 2. Leon with steve s. chung of national chiao-tung
university, steve and mia Kang, and Kamran Eshraghian of
the university of adelaide at the 2nd memristors and memristive systems symposium.

Achievement, which contained celebratory letters from
virtually all "who's who"s worldwide in the Circuits and
Systems Community. In one note, Charles A. Desoer
wrote, "...Leon has been a continuous source of ideas
of techniques and problems. His work on chaos is very
interesting; in particular his third order circuit which exhibits chaos and is so easily visualizable is a jewel. Leon
has had a considerable impact on circuit theory by his
own work and of his students." Michael Peter Kennedy
wrote, "... It is hard, listening to Leon's lecture and not
to be seduced by his enthusiasm for nonlinear circuits.
He has devoted his life to understanding and explaining
the mysteries of nonlinearity in all manifestations, and to
inspiring others to share his blue sky dreams." That was
more than two decades ago. Leon's scholarly contributions and inspiring the community have snowballed
marvelously with never-ending passion. In 2008 after
more than 35 years from Leon's memristor discovery
IEEE cIrcuIts and systEms magazInE

Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q2 2018