7.7 Examples on Memristor Circuit Programming
305
Fig. 7.10 Bifurcation induced by the pulse in Fig. 7.8 with A = 0.00781. The double-scroll
chaotic attractor turns into a period-three limit cycle. The black curve represents the period-three
limit cycle when τ ∈ [900, 1000]
f (ϕ M1 )
C
R
e(t)
a(t)
L
h (q M2 )
−
+
v C
−
+
i L
Fig. 7.11 A circuit with two memristors
7.7.2 Circuit with Two Memristors
Consider as in Fig. 7.11 a circuit with a flux-controlled memristor q M 1 = f (ϕ M 1 ),
a charge-controlled memristor ϕ M 2 = h(q M 2 ), a current source a(t), and a voltage
source e(t) introduced from programming purposes. It is easily seen that the circuit
satisfies assumptions (A1)–(A3) for the existence of the SE representation in the
(ϕ, q)-domain. We have n x = 2, n = n C + n L = 2, hence n y = 0 so that we are in
the case considered in Sect. 7.5.3. Then, H = H 11 , whereas matrices H 12 , H 21 and
H 22 are not present. Similarly, u(t) = u x (t), whereas u y (t) is not present. A simple
circuit analysis yields the hybrid representation with
305
Fig. 7.10 Bifurcation induced by the pulse in Fig. 7.8 with A = 0.00781. The double-scroll
chaotic attractor turns into a period-three limit cycle. The black curve represents the period-three
limit cycle when τ ∈ [900, 1000]
f (ϕ M1 )
C
R
e(t)
a(t)
L
h (q M2 )
−
+
v C
−
+
i L
Fig. 7.11 A circuit with two memristors
7.7.2 Circuit with Two Memristors
Consider as in Fig. 7.11 a circuit with a flux-controlled memristor q M 1 = f (ϕ M 1 ),
a charge-controlled memristor ϕ M 2 = h(q M 2 ), a current source a(t), and a voltage
source e(t) introduced from programming purposes. It is easily seen that the circuit
satisfies assumptions (A1)–(A3) for the existence of the SE representation in the
(ϕ, q)-domain. We have n x = 2, n = n C + n L = 2, hence n y = 0 so that we are in
the case considered in Sect. 7.5.3. Then, H = H 11 , whereas matrices H 12 , H 21 and
H 22 are not present. Similarly, u(t) = u x (t), whereas u y (t) is not present. A simple
circuit analysis yields the hybrid representation with