xviii
Preface
New peculiar and intriguing dynamical features of memristor circuits, such
as the presence of invariant manifolds, coexisting dynamics and attractors
(extreme multistability), and bifurcations without parameters, are addressed and
characterized analytically.
Finally, Chap. 7 develops a systematic analytic procedure for programming
different dynamics and regimes in non-autonomous memristor circuits by means
of impulsive voltage or current sources.
Applications and Extension of the FCAM
Chapter 8 describes the application of FCAM to study synchronization phenomena
in arrays of locally connected oscillators, while Chap. 9 exploits FCAM to design
a class of memristor neural networks that are able to process signals in the (ϕ, q)domain according to the principle of in-memory computing.
Chapter 10 develops a circuit model of a class of extended memristors by
interconnecting basic circuit elements as an ideal memristor and a nonlinear resistor.
FCAM is then used to analyze the dynamics in the case the nonlinear resistor
has a piecewise-linear voltage-current characteristic. Finally, Chap. 11 discusses the
extension of FCAM to nonlinear circuits containing also higher-order elements such
as memcapacitors and meminductors, showing that such circuits display even richer
dynamic features with respect to memristor circuits.
Prerequisites and Audience
From a didactic viewpoint, the present book is intended for a graduate-level course
in engineering on memristors including relevant aspects of nonlinear circuit theory
connected with the emerging nanoscale devices. It may also be used for self-study
or as a reference book by engineers, physicists, and applied mathematicians. From
a research viewpoint, the book is an account of the state of the art on some main
research directions in the analysis of memristor circuits. As such it may be used as
a solid basis to start and pursue researches on the challenging and rapidly evolving
field of memristors and nanoscale devices.
The prerequisite of this book is a graduate-level course in circuit theory
introducing basic aspects of the analysis of nonlinear circuits at the level of classical
textbooks (e.g., [22]). The needed mathematical background corresponds to the
essential level of calculus, ordinary differential equations, and algebra that are
part of the graduate student curricula in engineering, physics, and mathematics.
Whenever possible, mathematics is kept to a minimum without losing rigor and
accuracy in the description. Ad hoc mathematical textbooks are adequately referred
to in order to give the reader the possibility to further elaborate on some of the
presented topics.
Preface
New peculiar and intriguing dynamical features of memristor circuits, such
as the presence of invariant manifolds, coexisting dynamics and attractors
(extreme multistability), and bifurcations without parameters, are addressed and
characterized analytically.
Finally, Chap. 7 develops a systematic analytic procedure for programming
different dynamics and regimes in non-autonomous memristor circuits by means
of impulsive voltage or current sources.
Applications and Extension of the FCAM
Chapter 8 describes the application of FCAM to study synchronization phenomena
in arrays of locally connected oscillators, while Chap. 9 exploits FCAM to design
a class of memristor neural networks that are able to process signals in the (ϕ, q)domain according to the principle of in-memory computing.
Chapter 10 develops a circuit model of a class of extended memristors by
interconnecting basic circuit elements as an ideal memristor and a nonlinear resistor.
FCAM is then used to analyze the dynamics in the case the nonlinear resistor
has a piecewise-linear voltage-current characteristic. Finally, Chap. 11 discusses the
extension of FCAM to nonlinear circuits containing also higher-order elements such
as memcapacitors and meminductors, showing that such circuits display even richer
dynamic features with respect to memristor circuits.
Prerequisites and Audience
From a didactic viewpoint, the present book is intended for a graduate-level course
in engineering on memristors including relevant aspects of nonlinear circuit theory
connected with the emerging nanoscale devices. It may also be used for self-study
or as a reference book by engineers, physicists, and applied mathematicians. From
a research viewpoint, the book is an account of the state of the art on some main
research directions in the analysis of memristor circuits. As such it may be used as
a solid basis to start and pursue researches on the challenging and rapidly evolving
field of memristors and nanoscale devices.
The prerequisite of this book is a graduate-level course in circuit theory
introducing basic aspects of the analysis of nonlinear circuits at the level of classical
textbooks (e.g., [22]). The needed mathematical background corresponds to the
essential level of calculus, ordinary differential equations, and algebra that are
part of the graduate student curricula in engineering, physics, and mathematics.
Whenever possible, mathematics is kept to a minimum without losing rigor and
accuracy in the description. Ad hoc mathematical textbooks are adequately referred
to in order to give the reader the possibility to further elaborate on some of the
presented topics.