6.1 First-Order Memristor Circuits
231
−3
−2
−1
1
2
3
−2
−1
1
2
◦
•
•
Q 0 = 0
¯
ϕ
α
M
¯
ϕ
β
M
¯
ϕ
γ
M
ϕ M
dϕM
dt
−3
−2
−1
1
2
3
−2
−1
1
2
◦
•
•
Q 0 =
1
3
¯
ϕ
α
M ¯
ϕ
β
M
¯
ϕ
γ
M
ϕ M
dϕM
dt
−3
−2
−1
1
2
3
−2
−1
1
2
•
×
Q 0 =
2
3
¯
ϕ
αβ
M
¯
ϕ
γ
M
ϕ M
dϕM
dt
−3
−2
−1
1
2
3
−2
−1
1
2
•
Q 0 = 1
¯
ϕ
γ
M
ϕ M
dϕM
dt
Fig. 6.10 Dynamic route of (6.13) for various values of Q 0 and the cubic nonlinearity (6.15) with
a = 1 and b = 1/3. We have Q sn
0 = 2/3
1. If Q 0 > Q sn
0 , we have Δ > 0 and ˆ
σ is real. Then, there is a unique EP
¯
ϕ
γ
M =
a
3b ˆ
σ
+ ˆ
σ .
2. Similarly, if Q 0 < −Q sn
0 , there is a unique EP
¯
ϕ
α
M = −
a
3b ˆ
σ
− ˆ
σ .
3. If Q 0 = Q sn
0 , then Δ = 0 and again ˆ
σ is real. There are two EPs given by
¯
ϕ
αβ
M = −
a
3b