IEEE Circuits and Systems Magazine - Q2 2018 - 15

One of the most important feature of the 4-lobe Chua corsage
memristor is the contiguousness of its multiple
extremum point DC V-I curve.

contains a simpler state equation along with a less
complex small-signal equivalent circuit model than the
second-order locally-active memristor proposed in [2].
Moreover, the dynamic routes of our generic memristor
exhibits more equilibrium points than those in the 2-lobe
Chua corsage memristor in [3]. The newly designed generic memristor exhibits a variety of dynamic routes in
response to different initial conditions. One of the most
important feature of the 4-lobe Chua corsage memristor
is the contiguousness of its multiple extremum point DC V-I
curve. In contrast, most published highly-nonlinear DC V-I
curves have several disconnected branches. Moreover, the
DC V-I curve of the 4-lobe Chua corsage memristor contains a negative-slope region which can give rise to various
complex phenomena by exploiting its local activity and
edge of chaos regime. However, similar to other first-order
locally-active memristors, the poles of the admittance of
4-lobe Chua corsage memristor lies on the open left-half
plane for which it needs at least one energy storage element to generate oscillation. The type and the value of the
energy storage element can be determined by analyzing
the frequency response of the small-signal admittance
function and by specifying the oscillation frequency. The
oscillating frequency must be specified in such a way that
the real part of the small-signal admittance function remains zero when the imaginary part is nonzero [3]. The
nonzero imaginary part of the admittance calculated at
the oscillating frequency is the determining factor of the
type and value of the energy storage element.
The series combination of the 4-lobe Chua corsage
memristor and the energy storage element along with
a battery provide a second-order state equations. The
poles of the admittance function of the composite 1-port
N migrates in the open right-half plane as well as on the
imaginary axis in the pole-zero diagram. The migration
of the poles of the composite admittance to the imaginary axis gives rise to a small-sinusoidal oscillation via a
super-critical Hopf bifurcation. Moreover, due to the external inductance, the total impedance of the composite
1-port N tends to zero at the operating point, thereby
giving rise to a small sinusoidal oscillation.

The 4-lobe Chua corsage memristor and its properties are described in section II. A description of our oscillator circuit are given in section III and verification of
the oscillation along with its nonlinear dynamical basis,
namely, local activity, edge of chaos, and Hopf bifurcation are given in section IV. Section V shows the limit
cycle generated by our oscillator circuit. The conclusion
is given in section V.
II. 4-lobe Chua Corsage Memristor
The 4-lobe Chua corsage memristor is a first-order locally active generic [4] memristor constructed on the
basis of the 2-lobe Chua corsage memristor [3], as shown
in Fig. 1. The state-dependent Ohm's law and the simple
state equation of the 4-lobe Chua corsage memristor is
defined by,
State-Dependent Ohm's Law:
i = G (x)v,

(1)

G (x) = G 0 x 2,

(2)

dx = f (x) + v
dt

(3)

where

State Equation:

where
f (x) = 59 - x + x - 20 - x - 40 + x - 65 - x - 95 . (4)

4-Lobe Chua Corsage
Memristor
i
+
v
_

G (x )

State-Dependent Ohm's Law:
i = G (x )v
State Equation:
dx = f (x ) + v
dt

Figure 1. definition of the 4-lobe chua corsage memristor,
where G (x) and f (x) are defined by (2) and (4), respectively.

Z. I. Mannan and C. Yang are with the Division of Electronic and Information Engineering and Artificial Intelligent Center (AIC), Chonbuk National University, Jeonju, Jeonbuk, 567-54896, Republic of Korea (e-mail: zimannan@gmail.com, ychangju@jbnu.ac.kr). H. Kim (Corresponding author) is with the
Division of Electronic Engineering, Intelligent Robots Research Center, and Artificial Intelligent Center (AIC), Chonbuk National University, Jeonju, Jeonbuk, 567-54896, Republic of Korea (e-mail: hskim@jbnu.ac.kr). This work was supported in part by the National Research Foundation of Korea (NRF)
grant funded by the Korea government (2016R1A2B4015514) and the USA Air Force office of Scientific Research under Grant number FA9550-18-1-0016.
sEcOnd quartEr 2018

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