xvi
Preface
The authors’ aim is to make clear to the readers that there are several main
advantages when using FCAM with respect to the traditional analysis in the voltagecurrent domain. Two key advantages are related to the principle of reduction of order
for the dynamics and the possibility to deal with a smoother dynamics, in the (ϕ, q)domain, with respect to the (v, i)-domain. In addition, any fundamental property of
a memristor circuit proved via FCAM in the (ϕ, q)-domain has a corresponding one
for an RLC circuit in the (v, i)-domain. Via this analogy, systematic methods for
writing the dynamic equations of memristor circuits in the form of a Differential
Algebraic Equation (DAE), or a State Equation (SE), are developed.
Moreover, FCAM permits to highlight and rigorously show the existence of
new peculiar dynamic behaviors displayed by memristor circuits. These include the
presence of invariant manifolds and the coexistence of different nonlinear dynamics,
attractors, and regimes, a complex dynamic scenario that is sometimes referred to
in the literature as extreme multistability. The coexistence of different attractors
is shown to be related to a new type of bifurcations, due to changing the initial
conditions for a fixed set of circuit parameters, which are named bifurcations
without parameters.
Given the extremely rich dynamic scenario in memristor circuits, it is natural to
wonder if there is the possibility to control and programme different attractors and
regimes in an effective way. This book shows that there is a positive answer to this
question by developing a simple programming procedure using impulsive voltage
or current sources (a natural way for transmitting signals from a neuromorphic
viewpoint).
Applications of the results are considered to oscillatory and chaotic memristor
circuits and also to arrays of memristor oscillators and neuromorphic architectures.
Finally, FCAM is generalized to higher-order elements with memory (also named
mem-elements) as memcapacitors and meminductors and also to some classes of
extended memristors.
Next, we discuss in some more detail the organization of the book, the content
of each single chapter, and the prerequisites and the audience for which the book is
intended.
We then conclude the preface by reporting a slightly abridged version of an article
by Chua [21] devoted to a reminiscence of the genesis and the thought process he
followed to theoretically introduce the fourth circuit element.
Organization of the Book
The book is mainly organized in three parts:
• Foundation of Nonlinear Circuit Theory
• Flux-Charge Analysis Method (FCAM)
• Applications and Extension of FCAM
Preface
The authors’ aim is to make clear to the readers that there are several main
advantages when using FCAM with respect to the traditional analysis in the voltagecurrent domain. Two key advantages are related to the principle of reduction of order
for the dynamics and the possibility to deal with a smoother dynamics, in the (ϕ, q)domain, with respect to the (v, i)-domain. In addition, any fundamental property of
a memristor circuit proved via FCAM in the (ϕ, q)-domain has a corresponding one
for an RLC circuit in the (v, i)-domain. Via this analogy, systematic methods for
writing the dynamic equations of memristor circuits in the form of a Differential
Algebraic Equation (DAE), or a State Equation (SE), are developed.
Moreover, FCAM permits to highlight and rigorously show the existence of
new peculiar dynamic behaviors displayed by memristor circuits. These include the
presence of invariant manifolds and the coexistence of different nonlinear dynamics,
attractors, and regimes, a complex dynamic scenario that is sometimes referred to
in the literature as extreme multistability. The coexistence of different attractors
is shown to be related to a new type of bifurcations, due to changing the initial
conditions for a fixed set of circuit parameters, which are named bifurcations
without parameters.
Given the extremely rich dynamic scenario in memristor circuits, it is natural to
wonder if there is the possibility to control and programme different attractors and
regimes in an effective way. This book shows that there is a positive answer to this
question by developing a simple programming procedure using impulsive voltage
or current sources (a natural way for transmitting signals from a neuromorphic
viewpoint).
Applications of the results are considered to oscillatory and chaotic memristor
circuits and also to arrays of memristor oscillators and neuromorphic architectures.
Finally, FCAM is generalized to higher-order elements with memory (also named
mem-elements) as memcapacitors and meminductors and also to some classes of
extended memristors.
Next, we discuss in some more detail the organization of the book, the content
of each single chapter, and the prerequisites and the audience for which the book is
intended.
We then conclude the preface by reporting a slightly abridged version of an article
by Chua [21] devoted to a reminiscence of the genesis and the thought process he
followed to theoretically introduce the fourth circuit element.
Organization of the Book
The book is mainly organized in three parts:
• Foundation of Nonlinear Circuit Theory
• Flux-Charge Analysis Method (FCAM)
• Applications and Extension of FCAM