538 research outputs found
Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria
A model of memristor-based Chuas oscillator is studied. The considered system
has infinitely many equilibrium points, which build a line of equilibria.
Bifurcational mechanisms of oscillation excitation are explored for different
forms of nonlinearity. Hard and soft excitation scenarios have principally
different nature. The hard excitation is determined by the memristor
piecewise-smooth characteristic and is a result of a border-collision
bifurcation. The soft excitation is caused by addition of a smooth nonlinear
function and has distinctive features of the supercritical Andronov-Hopf
bifurcation. Mechanisms of instability and amplitude limitation are described
for both two cases. Numerical modelling and theoretical analysis are combined
with experiments on an electronic analog model of the system under study. The
issues concerning physical realization of the dynamics of systems with a line
of equilibria are considered. The question on whether oscillations in such
systems can be classified as the self-sustained oscillations is raised.Comment: 14 pages, 5 figure
Andronov-Hopf bifurcation with and without parameter in a cubic memristor oscillator with a line of equilibria
The model of a memristor-based oscillator with cubic nonlinearity is studied.
The considered system has infinitely many equilibrium points, which build a
line of equilibria in the phase space. Numerical modeling of the dynamics is
combined with bifurcational analysis. It is shown that oscillation excitation
has distinctive features of the supercritical Andronov--Hopf bifurcation and
can be achieved by changing of a parameter value as well as by variation of
initial conditions. Therefore the considered bifurcation is called
Andronov-Hopf bifurcation with and without parameter.Comment: 3 figures. arXiv admin note: substantial text overlap with
arXiv:1705.0630
Bifurcation set for a disregarded Bogdanov-Takens unfolding. Application to 3D cubic memristor oscillators
We derive the bifurcation set for a not previously considered
three-parametric Bogdanov-Takens unfolding, showing that it is possible express
its vector field as two different perturbed cubic Hamiltonians. By using
several first-order Melnikov functions, we obtain for the first time analytical
approximations for the bifurcation curves corresponding to homoclinic and
heteroclinic connections, which along with the curves associated to local
bifurcations organize the parametric regions with different structures of
periodic orbits.
As an application of these results, we study a family of 3D memristor
oscillators, for which the characteristic function of the memristor is a cubic
polynomial. We show that these systems have an infinity number of invariant
manifolds, and by adding one parameter that stratifies the 3D dynamics of the
family, it is shown that the dynamics in each stratum is topologically
equivalent to a representant of the above unfolding. Also, based upon the
bifurcation set obtained, we show the existence of closed surfaces in the 3D
state space which are foliated by periodic orbits. Finally, we clarify some
misconceptions that arise from the numerical simulations of these systems,
emphasizing the important role played by the existence of invariant manifolds.Comment: 24 pages, 10 figures, submitted to Nonlinearit
Recent Advances in Physical Reservoir Computing: A Review
Reservoir computing is a computational framework suited for
temporal/sequential data processing. It is derived from several recurrent
neural network models, including echo state networks and liquid state machines.
A reservoir computing system consists of a reservoir for mapping inputs into a
high-dimensional space and a readout for pattern analysis from the
high-dimensional states in the reservoir. The reservoir is fixed and only the
readout is trained with a simple method such as linear regression and
classification. Thus, the major advantage of reservoir computing compared to
other recurrent neural networks is fast learning, resulting in low training
cost. Another advantage is that the reservoir without adaptive updating is
amenable to hardware implementation using a variety of physical systems,
substrates, and devices. In fact, such physical reservoir computing has
attracted increasing attention in diverse fields of research. The purpose of
this review is to provide an overview of recent advances in physical reservoir
computing by classifying them according to the type of the reservoir. We
discuss the current issues and perspectives related to physical reservoir
computing, in order to further expand its practical applications and develop
next-generation machine learning systems.Comment: 62 pages, 13 figure
PPV modelling of memristor-based oscillator
In this letter, we propose for the first time a method of abstracting the PPV
(Perturbation Projection Vector) characteristic of the up-to-date
memristor-based oscillators. Inspired from biological oscillators and its
characteristic named PRC (Phase Response Curve), we build a bridge between PRC
and PPV. This relationship is verified rigorously using the transistor level
simulation of Colpitts and ring oscillators, i.e., comparing the PPV converted
from PRC and the PPV obtained from accurate PSS+PXF simulation. Then we apply
this method to the PPV calculation of the memristor-based oscillator. By
keeping the phase dynamics of the oscillator and dropping the details of
voltage/current amplitude, the PPV modelling is highly efficient to describe
the phase dynamics due to the oscillator coupling, and will be very suitable
for the fast simulation of large scale oscillatory neural networks
Memristive Sisyphus circuit for clock signal generation
Frequency generators are widely used in electronics. Here, we report the
design and experimental realization of a memristive frequency generator
employing a unique combination of only digital logic gates, a single-supply
voltage and a realistic threshold-type memristive device. In our circuit, the
oscillator frequency and duty cycle are defined by the switching
characteristics of the memristive device and external resistors. We demonstrate
the circuit operation both experimentally, using a memristor emulator, and
theoretically, using a model memristive device with threshold. Importantly,
nanoscale realizations of memristive devices offer small-size alternatives to
conventional quartz-based oscillators. In addition, the suggested approach can
be used for mimicking some cyclic (Sisyphus) processes in nature, such as
"dripping ants" or drops from leaky faucets.Comment: 7 pages, 4 figure
Spin torque building blocks
The discovery of the spin torque effect has made magnetic nanodevices
realistic candidates for active elements of memory devices and applications.
Magnetoresistive effects allow the read-out of increasingly small magnetic
bits, and the spin torque provides an efficient tool to manipulate - precisely,
rapidly and at low energy cost - the magnetic state, which is in turn the
central information medium of spintronic devices. By keeping the same magnetic
stack, but by tuning a device's shape and bias conditions, the spin torque can
be engineered to build a variety of advanced magnetic nanodevices. Here we show
that by assembling these nanodevices as building blocks with different
functionalities, novel types of computing architectures can be envisisaged. We
focus in particular on recent concepts such as magnonics and spintronic neural
networks
Discontinuity Induced Hopf and Neimark-Sacker Bifurcations in a Memristive Murali-Lakshmanan-Chua Circuit
We report using Clarke's concept of generalised differential and a
modification of Floquet theory to non-smooth oscillations, the occurrence of
discontinuity induced Hopf bifurcations and Neimark-Sacker bifurcations leading
to quasiperiodic attractors in a memristive Murali-Lakshmanan-Chua (memristive
MLC) circuit. The above bifurcations arise because of the fact that a
memristive MLC circuit is basically a nonsmooth system by virtue of having a
memristive element as its nonlinearity. The switching and modulating properties
of the memristor which we have considered endow the circuit with two
discontinuity boundaries and multiple equilibrium points as well. As the
Jacobian matrices about these equilibrium points are non-invertible, they are
non-hyperbolic, some of these admit local bifurcations as well. Consequently
when these equilibrium points are perturbed, they lose their stability giving
rise to quasiperiodic orbits. The numerical simulations carried out by
incorporating proper discontinuity mappings (DMs), such as the Poincar\'{e}
discontinuity map (PDM) and zero time discontinuity map (ZDM), are found to
agree well with experimental observations.Comment: 28 pages,18 figure
Experimental evidence of chaos from memristors
Until now, most memristor-based chaotic circuits proposed in the literature
are based on mathematical models which assume ideal characteristics such as
piece-wise linear or cubic non-linearities. The idea, illustrated here and
originating from the experimental approach for device characterization, is to
realize a chaotic system exploiting the non-linearity of only one memristor
with a very simple experimental set-up using feedback. In this way a simple
circuit is obtained and chaos is experimentally observed and is confirmed by
the calculation of the largest Lyapunov exponent. Numerical results using the
Strukov model support the existence of robust chaos in our circuit. This is the
first experimental demonstration of chaos in a real memristor circuit and
suggests that memristors are well placed for hardware encryption.Comment: Accepted for publication in International Journal of Bifurcation and
Chao
In-materio neuromimetic devices: Dynamics, information processing and pattern recognition
The story of information processing is a story of great success. Todays'
microprocessors are devices of unprecedented complexity and MOSFET transistors
are considered as the most widely produced artifact in the history of mankind.
The current miniaturization of electronic circuits is pushed almost to the
physical limit and begins to suffer from various parasitic effects. These facts
stimulate intense research on neuromimetic devices. This feature article is
devoted to various in materio implementation of neuromimetic processes,
including neuronal dynamics, synaptic plasticity, and higher-level signal and
information processing, along with more sophisticated implementations,
including signal processing, speech recognition and data security. Due to vast
number of papers in the field, only a subjective selection of topics is
presented in this review
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