11.6 Chaotic Circuit with Memcapacitor and Memristor
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Fig. 11.12 3D view of the trajectory evolution
Example 11.1 Consider a mem-element circuit as in Fig. 11.15 containing a twoterminal element, given by the parallel connection of a σ -controlled memcapacitor
and a flux-controlled memristor, and a linear inductor, connected to a two-port
network with only linear resistors and flux and charge independent sources.
The two-terminal element MC σ -M ϕ is not included in those considered in the
class LME (or in the class LME ). This notwithstanding, we wish to show that it
is still possible to derive the SE representation in the (ϕ, q)-domain.
Suppose there exists the hybrid representation of N R
q 1 (t; t 0 ) = h 11 ϕ 1 (t; t 0 ) + h 12 q 2 (t; t 0 ) + q a (t; t 0 )
ϕ 2 (t; t 0 ) = h 21 ϕ 1 (t; t 0 ) + h 22 q 2 (t; t 0 ) + ϕ e (t; t 0 ).
KϕL and KqL at port 1 yield
ϕ 1 (t; t 0 ) = ϕ MC (t; t 0 ) = ϕ M (t; t 0 ); q 1 (t; t 0 ) + q MC (t; t 0 ) + q M (t; t 0 ) = 0
and at port 2 we have
q 2 (t; t 0 ) = q L (t; t 0 ); ϕ 2 (t; t 0 ) = −ϕ L (t; t 0 ).
The CR of M ϕ is
q M (t; t 0 ) = f M (ϕ M (t; t 0 ) + ϕ M 0 ) − f M (ϕ M 0 )