344
9 Memristor Cellular Neural Networks Computing in the Flux-charge Domain
design procedure based on FCAM, and the use of a prototypical memristor as that
proposed by HP (cf. Chap. 2), we obtain an M-SCNN model that is the analogous
in the (ϕ, q)-domain of that describing the dynamics in the (v, i)-domain of a
SCNN. However, due to the use of memristors during the analog computation, MSCNNs display peculiar and basically different properties with respect to SCNNs,
as remarked next.
• One salient feature is that the analog processing of M-SCNNs takes place in the
(ϕ, q)-domain, instead of the typical (v, i)-domain, as it happens for SCNNs.
In the case of charge-controlled memristors, the inputs are provided via the
initial values of memristor charges q M i (0), the processing is accomplished during
the time evolutions of q M i (t), and the result of processing, for convergent MSCNNs, is given by the asymptotic values of charges q M i (∞) (or asymptotic
values of memristances).
• There are potential advantages in terms of power consumption for NNs operating
in the (ϕ, q)-domain. Indeed, when a steady state is reached, i.e., the memristor
charges reach a constant value, the memristor currents and voltages, as well as
the capacitors and all other voltages and currents in the M-SCNNs, vanish. Said
another way, at a steady state a M-SCNN turns off and so the dissipated power
is null. Yet, in steady state the memristors act as nonvolatile devices keeping in
memory the processing result, i.e., the asymptotic values of charges q M i (∞) (or
the corresponding memristances). We stress that this is different from SCNNs,
where voltages, currents, and power do not vanish when a steady state is reached,
and batteries are needed to hold in memory the processing result.
• In a M-SCNN the role played by memristors is twofold. They participate in the
nonlinear dynamics used for real-time signal processing and they also store the
result of computation in the asymptotic values of the charge. Namely, in a MSCNN, processing and storing of information are at the same physical location,
according to the principle of in-memory computing. This is a potential advantage
also with respect to traditional Von Neumann computing machines, where one
main bottleneck is due to the fact that processing and storing are at different
physical locations (e.g., the CPU and the RAM).
Since M-SCNNs are analogous from a mathematical viewpoint to SCNNs, it
is possible to exploit the bulk of results already available in the literature for
studying the dynamics of SCNNs in the (ϕ, q)-domain and to design them in order
to accomplish a large variety of signal processing tasks [9].
The chapter also gives a foundation to the nonlinear dynamics in the (ϕ, q)domain of the M-SCNN model and addresses convergence of solutions in the case
of symmetric interconnections between cells. Applications to the solution of some
simple image processing tasks in real time are also discussed to confirm that the
introduced model has processing capabilities analogous to those of a SCNN.
9 Memristor Cellular Neural Networks Computing in the Flux-charge Domain
design procedure based on FCAM, and the use of a prototypical memristor as that
proposed by HP (cf. Chap. 2), we obtain an M-SCNN model that is the analogous
in the (ϕ, q)-domain of that describing the dynamics in the (v, i)-domain of a
SCNN. However, due to the use of memristors during the analog computation, MSCNNs display peculiar and basically different properties with respect to SCNNs,
as remarked next.
• One salient feature is that the analog processing of M-SCNNs takes place in the
(ϕ, q)-domain, instead of the typical (v, i)-domain, as it happens for SCNNs.
In the case of charge-controlled memristors, the inputs are provided via the
initial values of memristor charges q M i (0), the processing is accomplished during
the time evolutions of q M i (t), and the result of processing, for convergent MSCNNs, is given by the asymptotic values of charges q M i (∞) (or asymptotic
values of memristances).
• There are potential advantages in terms of power consumption for NNs operating
in the (ϕ, q)-domain. Indeed, when a steady state is reached, i.e., the memristor
charges reach a constant value, the memristor currents and voltages, as well as
the capacitors and all other voltages and currents in the M-SCNNs, vanish. Said
another way, at a steady state a M-SCNN turns off and so the dissipated power
is null. Yet, in steady state the memristors act as nonvolatile devices keeping in
memory the processing result, i.e., the asymptotic values of charges q M i (∞) (or
the corresponding memristances). We stress that this is different from SCNNs,
where voltages, currents, and power do not vanish when a steady state is reached,
and batteries are needed to hold in memory the processing result.
• In a M-SCNN the role played by memristors is twofold. They participate in the
nonlinear dynamics used for real-time signal processing and they also store the
result of computation in the asymptotic values of the charge. Namely, in a MSCNN, processing and storing of information are at the same physical location,
according to the principle of in-memory computing. This is a potential advantage
also with respect to traditional Von Neumann computing machines, where one
main bottleneck is due to the fact that processing and storing are at different
physical locations (e.g., the CPU and the RAM).
Since M-SCNNs are analogous from a mathematical viewpoint to SCNNs, it
is possible to exploit the bulk of results already available in the literature for
studying the dynamics of SCNNs in the (ϕ, q)-domain and to design them in order
to accomplish a large variety of signal processing tasks [9].
The chapter also gives a foundation to the nonlinear dynamics in the (ϕ, q)domain of the M-SCNN model and addresses convergence of solutions in the case
of symmetric interconnections between cells. Applications to the solution of some
simple image processing tasks in real time are also discussed to confirm that the
introduced model has processing capabilities analogous to those of a SCNN.