Foreword by Ronald Tetzlaff
An increasing number of different two-terminal devices manufactured in distinct
technologies can be classified as memristors with most popular developments so
far, in technologies implementing dense, low-power nonvolatile memories and
neuromorphic systems operating according to biological principles. Especially,
recent investigations show a strong interest in new computing architectures required
for future digital systems that are often based on communicating intelligent sensor–
processor architectures. The development of new memristor computing concepts in
order to overcome the limits of classical technology caused by the so-called vonNeumann bottleneck is based on principles in which processing and data storage
are carried out in the same physical location. These technologies are ranging from
crossbar arrays to artificial and bio-inspired neural networks, including models
of biological computation in a human brain. The availability and application of
these so-called in-memory computing systems would obviate the need for energyexpensive data transfer operations on the memory-CPU in future IOT networks.
While different authors have shown in an increasing number of publications that certain mathematical operations can be performed rather efficiently on crossbar arrays,
attractive concepts of universal computation are based on the emergence of complex
behavior in strongly nonlinear dynamical arrays. By investigating the so-called
reaction–diffusion systems, Leon Chua has derived the fundamental results that
prove that the emergence of complexity in these structures is based on local activity
and in particular on a parameter subset called the “Edge of Chaos.” Typically,
the treatment of such highly nonlinear, memristive spatiotemporal systems, which
exhibit oscillations, pattern formation, and wave propagation phenomena, is based
on the availability of compact device models and on new mathematical strategies
to gain a deep understanding of the mechanisms of such systems in order to enable
the derivation of highly efficient in-memory computing methods. Although memelements and memristive circuits have been addressed in a bulk of publications,
an in-depth mathematical treatment and understanding based on circuit theory has
been provided in only a few investigations. Mostly, present model-based simulators
operating in the voltage-current domain make qualitatively incorrect predictions,
especially when applied to the problems of nonlinear dynamics. There is a lack
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An increasing number of different two-terminal devices manufactured in distinct
technologies can be classified as memristors with most popular developments so
far, in technologies implementing dense, low-power nonvolatile memories and
neuromorphic systems operating according to biological principles. Especially,
recent investigations show a strong interest in new computing architectures required
for future digital systems that are often based on communicating intelligent sensor–
processor architectures. The development of new memristor computing concepts in
order to overcome the limits of classical technology caused by the so-called vonNeumann bottleneck is based on principles in which processing and data storage
are carried out in the same physical location. These technologies are ranging from
crossbar arrays to artificial and bio-inspired neural networks, including models
of biological computation in a human brain. The availability and application of
these so-called in-memory computing systems would obviate the need for energyexpensive data transfer operations on the memory-CPU in future IOT networks.
While different authors have shown in an increasing number of publications that certain mathematical operations can be performed rather efficiently on crossbar arrays,
attractive concepts of universal computation are based on the emergence of complex
behavior in strongly nonlinear dynamical arrays. By investigating the so-called
reaction–diffusion systems, Leon Chua has derived the fundamental results that
prove that the emergence of complexity in these structures is based on local activity
and in particular on a parameter subset called the “Edge of Chaos.” Typically,
the treatment of such highly nonlinear, memristive spatiotemporal systems, which
exhibit oscillations, pattern formation, and wave propagation phenomena, is based
on the availability of compact device models and on new mathematical strategies
to gain a deep understanding of the mechanisms of such systems in order to enable
the derivation of highly efficient in-memory computing methods. Although memelements and memristive circuits have been addressed in a bulk of publications,
an in-depth mathematical treatment and understanding based on circuit theory has
been provided in only a few investigations. Mostly, present model-based simulators
operating in the voltage-current domain make qualitatively incorrect predictions,
especially when applied to the problems of nonlinear dynamics. There is a lack
ix