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7 Pulse Programming of Memristor Circuits
by inspection. Furthermore, invariant manifolds and the dynamics on manifolds
are obtained by relying on ad hoc mathematical manipulations of these SEs. Due
to the huge variety and complexity of memristor circuits encountered in different
applications (e.g., memristor synapses for neuromorphic systems, memristor-based
chaotic circuits for cryptography, memristor-based biosensors, etc.), it is desirable
to extend the results in Chap. 6 in order that they are applicable to a large class of
memristor circuits used in the technical applications.
The main contributions in this chapter are as follows:
(a) we identify a wide class of memristor circuits, of any order and with any number
of flux- or charge-controlled memristors, and introduce a systematic method
for writing in an explicit way the SEs, both in the (ϕ, q) and in the (v, i)domain. The conditions for the existence of the SEs for such class are easily
checkable (usually by inspection), since they are couched in topological terms.
The techniques overcome drawbacks of the analogous technique described in
Chap. 5, that was able in general only to yield the SE formulation in implicit
form.
(b) The obtained SEs have a relatively simple mathematical structure and, in
the autonomous case, under certain assumptions, a systematic method is
introduced to identify and write analytically the invariant manifolds, to show
the coexistence of different dynamics and to find the reduced-order dynamics
on each invariant manifold.
The results in (a) and (b) are then used and extended for addressing the
nonautonomous case, i.e., the case where time-varying independent sources are
present in the memristor circuit. In this regard, the chief contribution in the chapter
is as follows:
(c) we develop analytic results showing how invariant manifolds, different regimes
and reduced-order dynamics, and attractors of nonautonomous memristor
circuits, can be easily and effectively programmed by applying suitable charge
and/or flux pulses via time-varying current and/or voltage sources with finite
time duration.
For example, we have seen in Chap. 6 that in a given Memristor Chaotic Circuit
(MCC) built upon Chua’s oscillator there coexist stationary, periodic, and complex
attractors for the same set of parameters. We show in the chapter that, by means of a
single pulse source, it is possible to set in an effective way any desired stationary or
oscillatory regime in the MCC. This represents a significant practical improvement
with respect to results in Chap. 6, since in that case manifolds and reduced-order
dynamics were selected by imposing the whole set of four initial conditions for the
state variables of MCC in the (v, i)-domain.
Although we are dealing in this chapter with general circuits with an arbitrary
number of memristors, we find it useful for pedagogical reasons to first illustrate the
basic idea of pulse programming via a simple memristor circuit.
7 Pulse Programming of Memristor Circuits
by inspection. Furthermore, invariant manifolds and the dynamics on manifolds
are obtained by relying on ad hoc mathematical manipulations of these SEs. Due
to the huge variety and complexity of memristor circuits encountered in different
applications (e.g., memristor synapses for neuromorphic systems, memristor-based
chaotic circuits for cryptography, memristor-based biosensors, etc.), it is desirable
to extend the results in Chap. 6 in order that they are applicable to a large class of
memristor circuits used in the technical applications.
The main contributions in this chapter are as follows:
(a) we identify a wide class of memristor circuits, of any order and with any number
of flux- or charge-controlled memristors, and introduce a systematic method
for writing in an explicit way the SEs, both in the (ϕ, q) and in the (v, i)domain. The conditions for the existence of the SEs for such class are easily
checkable (usually by inspection), since they are couched in topological terms.
The techniques overcome drawbacks of the analogous technique described in
Chap. 5, that was able in general only to yield the SE formulation in implicit
form.
(b) The obtained SEs have a relatively simple mathematical structure and, in
the autonomous case, under certain assumptions, a systematic method is
introduced to identify and write analytically the invariant manifolds, to show
the coexistence of different dynamics and to find the reduced-order dynamics
on each invariant manifold.
The results in (a) and (b) are then used and extended for addressing the
nonautonomous case, i.e., the case where time-varying independent sources are
present in the memristor circuit. In this regard, the chief contribution in the chapter
is as follows:
(c) we develop analytic results showing how invariant manifolds, different regimes
and reduced-order dynamics, and attractors of nonautonomous memristor
circuits, can be easily and effectively programmed by applying suitable charge
and/or flux pulses via time-varying current and/or voltage sources with finite
time duration.
For example, we have seen in Chap. 6 that in a given Memristor Chaotic Circuit
(MCC) built upon Chua’s oscillator there coexist stationary, periodic, and complex
attractors for the same set of parameters. We show in the chapter that, by means of a
single pulse source, it is possible to set in an effective way any desired stationary or
oscillatory regime in the MCC. This represents a significant practical improvement
with respect to results in Chap. 6, since in that case manifolds and reduced-order
dynamics were selected by imposing the whole set of four initial conditions for the
state variables of MCC in the (v, i)-domain.
Although we are dealing in this chapter with general circuits with an arbitrary
number of memristors, we find it useful for pedagogical reasons to first illustrate the
basic idea of pulse programming via a simple memristor circuit.