7.3 Structure of Memristor Network and Differential Algebraic Equation. . .
281
• D
q
R ∈ N D . The CRs are
− ϕ λ R (t; t 0 ) = L λ R ˙
q λ R (t; t 0 ) − ϕ L λ R
(t 0 ) + R λ R q λ R (t; t 0 )
(7.6)
where ϕ L λ R
(t 0 ) are the ICs of inductors in D
q
R .
• D
q
L ∈ N D . The CRs are
− ϕ λ L (t; t 0 ) = L λ L ˙
q λ L (t; t 0 ) − ϕ L λ L
(t 0 )
(7.7)
where ϕ L λ L
(t 0 ) are the ICs of inductors in D
q
L .
Concerning the CRs of elements in N A we have the following.
• A
ϕ
M ∈ N A have CRs
− q μ F (t; t 0 ) = f(ϕ μ F (t; t 0 ) + ϕ M μ F
(t 0 )) − f(ϕ M μ F
(t 0 ))
(7.8)
where ϕ M μ F
(t 0 ) are the ICs of memristors in A
ϕ
M .
• A
q
M ∈ N A have CRs
− ϕ μ Q (t; t 0 ) = h(q μ Q (t; t 0 ) + q M μ Q (t 0 )) − h(q M μ Q (t 0 ))
(7.9)
where q M μ Q (t 0 ) are the ICs of memristors in A
q
M .
• A
ϕ
G ∈ N A have CRs
− q ρ G (t; t 0 ) = G ρ G ϕ ρ G (t; t 0 )
(7.10)
• A
q
R ∈ N A have CRs
− ϕ ρ R (t; t 0 ) = R ρ R q ρ R (t; t 0 ).
(7.11)
7.3.2 Hybrid Representation of N R
Among the different representations of the linear (n C +n L )-port N R , it is convenient
to exploit its hybrid description (cf. Remark 3.8 in Chap. 4)