IEEE Circuits and Systems Magazine - Q2 2018 - 66

1.2

0.8

0.8
0.6

x0 = 0.85

x0 = 0.75

0.6
x

x

x0 = 0.9
x0 = 0.8
x0 = 0.75
x0 = 0.6
x0 = 0.5
x0 = 0.25

1.0

x0 = 0.95

1

0.4

0.4

0.2

0.2

0

x0 = 0.65
0

2

0
4

t /s
(a)

6

8

10

x0 = 0
0

5

10

1
x0 = 0.95

3

x0 = 0
x0 = 0.25
x0 = 0.75 x = 0.8
0

2

-1

x0 = 0.75
vm ,M /V

vm ,M /V

0

x0 = 0.85

-2
-3

x0 = 0.65

-4
0

2

1

4

t /s
(b)

6

8

im /µA

im /µA

x0 = 0.85

4

t /s
(c)

6

15
t /s
(b)

20

30

x0 = 0.9

x0 = 0.6 x0 = 0.8
0
x0 = 0

x0 = 0.95
2

25

x0 = 0.9

x0 = 0.5
x0 = 0.2
0.25

100

x0 = 0.75

0

30

-1
x0 = 0.6
-3 x0 = 0.5
0
10
5

10

-100
-150

25

-2

x0 = 0.65

-50

20

0

50
0

15
t /s
(a)

8

10

x0 = 0.75

-100

Figure 25. Evidence for dc fading memory in the 1r1m structure. response to a negative voltage Vm = - 3 V. state (a),
voltage v m, M (b), and current i m (c) over time for initial conditions within the set defined as x 0 ! " 0.65, 0.75, 0.85, 0.95 , .

0

5

10

15
t /s
(c)

20

25

30

-20
-3

-2

-1

0
vm,M /V
(d)

1

2

3

40

depict the time response of the memory state x, of the
voltage v m, M across the nano-device, and of the current
i m through the series one-port to the application of a
triangular voltage waveform-of amplitude vt m = 2.95 V,
period T = 5 s, and positive polarity over the first half
cycle-across the composite two-terminal element
for all initial states within the closed set defined as
x 0 ! {0, 0.25, 0.5, 0.6, 0.75, 0.8, 0.9}. Irrespective of the
initial condition, there exists a unique asymptotic behaviour. The lower plateau of the oscillatory waveform
illustrated in plot (a) is the lower bound in the state existence domain. This is the direct consequence for the
faster switching kinetics the 1R1M structure exhibits under negative stimuli as compared to the case where it is
66

IEEE cIrcuIts and systEms magazInE

im /µA

20

0

Figure 26. Evidence for ac fading memory in the 1r1m
structure. response to a triangular voltage waveform of
amplitude vt m = 2.95 V, period T = 5 s, and positive polarity
over the first half cycle. state over time (a), voltage v m, M over
time (b), current i m over time (c), and current i m versus voltage v m, M (d) for initial conditions within the set defined as
x 0 ! " 0, 0.25, 0.5, 0.6, 0.75, 0.8, 0.9 , .

sEcOnd quartEr 2018



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