IEEE Circuits and Systems Magazine - Q2 2018 - 43
a nonlinear differential equation, which includes the
observable I/O variables u and y and their derivatives
[27], [28]. This equation is equivalent to an integro-differential equation for i and v, formalized by the generally nonlinear function F
3
40
1.5
20
0
0
-1.5
-20
-3
-40
0
0.5
1
1.5
2
0
0.5
t (s)
1
1.5
2
2
4
1.5
2
i (mA)
v (V)
and b being integers. Eq. (8) can be analyzed in relation
to the homothety fingerprint the same way as Eq. (2)
for the memristive systems. However, it is possible to
choose another approach. It is well known that the state
description (8) can be transformed into the I/O form as
t (s)
40
i (mA)
20
0
-20
-40
-4
-2
0
2
4
-4
-2
v (V)
0
v (V)
R M (kΩ)
1
0.5
0
0
0.5
1
1.5
2
0
0.5
1
t (s)
t (s)
(a)
(b)
Figure 6. Behavior of the system from Fig. 5 driven by sinusoidal voltage with zero initial flux. the voltage has an amplitude of n
Volts and a frequency of n Hz, where n = 1 (a) and n = 3 (b). the circuit parameters are: R on = 100 X, R off = 1 kX, { p = 0.1 Vs,
{ n = 0.25 Vs. the current (top Fig.) and memristance (bottom Fig.) waveforms exhibit switching processes caused by crossing
the flux via the threshold level, which is however modified by the sign of the derivative of voltage. accelerating and amplifying the
voltage 3 times results in amplifying the current 3 times without affecting its shape, and the area within the pinched hysteresis loop
is increased 9 times. the shape of the loop is also preserved.
SECOND quartEr 2018
IEEE CIrCuItS aND SyStEmS magazINE
43
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