Chapter 7
Pulse Programming of Memristor
Circuits
7.1 Introduction
Chapter 5 introduced the “Flux-Charge Analysis Method” (FCAM) for the dynamic
analysis of memristor circuits in the (ϕ, q)-domain. FCAM is based on using
Kirchhoff flux and charge laws, and CRs of circuit elements, directly expressed in
the (ϕ, q)-domain and, as such, it basically differs from other traditional approaches
for analyzing memristor circuits described in the (v, i)-domain [1–3].
Then, in Chap. 6, the application of FCAM to specific low-order autonomous
circuits with one memristor has shown that the state space in the (v, i)-domain
can be foliated in a continuum of positively invariant manifolds and that on each
manifold a memristor circuit is characterized by a different reduced-order dynamics
and attractors. A relevant consequence is that there coexist different nonlinear
dynamics and regimes for the same set of circuit parameters. Moreover, bifurcations
may be induced in two different ways. In the classical way, where the circuit
parameters are changed for initial conditions (ICs) belonging to a fixed manifold
(standard bifurcations). Otherwise, by changing invariant manifold via the variation
of ICs for fixed circuit parameters (also named bifurcations without parameters). In
particular, in Chap. 5, FCAM is used to analyze saddle-node bifurcations without
parameters for the simplest memristor circuit composed by a capacitor and a
flux-controlled memristor, and the Hopf and period-doubling bifurcations without
parameters for some memristor oscillatory circuits. Overall, these results have
provided an analytic explanation of novel and intriguing dynamic phenomena
displayed by memristor circuits, as the coexistence of several attractors for the same
set of parameters and the strong dependence upon ICs of the dynamic behavior
of solutions. We stress that such phenomena have been investigated elsewhere in
the literature mainly via numerical, or experimental means, see, e.g., [4–11], and
references therein.
In Chap. 6, only specific low-order autonomous circuits with one memristor
have been considered for which the state equations (SEs) are written via FCAM
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_7
271
Pulse Programming of Memristor
Circuits
7.1 Introduction
Chapter 5 introduced the “Flux-Charge Analysis Method” (FCAM) for the dynamic
analysis of memristor circuits in the (ϕ, q)-domain. FCAM is based on using
Kirchhoff flux and charge laws, and CRs of circuit elements, directly expressed in
the (ϕ, q)-domain and, as such, it basically differs from other traditional approaches
for analyzing memristor circuits described in the (v, i)-domain [1–3].
Then, in Chap. 6, the application of FCAM to specific low-order autonomous
circuits with one memristor has shown that the state space in the (v, i)-domain
can be foliated in a continuum of positively invariant manifolds and that on each
manifold a memristor circuit is characterized by a different reduced-order dynamics
and attractors. A relevant consequence is that there coexist different nonlinear
dynamics and regimes for the same set of circuit parameters. Moreover, bifurcations
may be induced in two different ways. In the classical way, where the circuit
parameters are changed for initial conditions (ICs) belonging to a fixed manifold
(standard bifurcations). Otherwise, by changing invariant manifold via the variation
of ICs for fixed circuit parameters (also named bifurcations without parameters). In
particular, in Chap. 5, FCAM is used to analyze saddle-node bifurcations without
parameters for the simplest memristor circuit composed by a capacitor and a
flux-controlled memristor, and the Hopf and period-doubling bifurcations without
parameters for some memristor oscillatory circuits. Overall, these results have
provided an analytic explanation of novel and intriguing dynamic phenomena
displayed by memristor circuits, as the coexistence of several attractors for the same
set of parameters and the strong dependence upon ICs of the dynamic behavior
of solutions. We stress that such phenomena have been investigated elsewhere in
the literature mainly via numerical, or experimental means, see, e.g., [4–11], and
references therein.
In Chap. 6, only specific low-order autonomous circuits with one memristor
have been considered for which the state equations (SEs) are written via FCAM
© Springer Nature Switzerland AG 2021
F. Corinto et al., Nonlinear Circuits and Systems with Memristors,
https://doi.org/10.1007/978-3-030-55651-8_7
271