3,350 research outputs found
Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise
We study associative memory based on temporal coding in which successful
retrieval is realized as an entrainment in a network of simple phase
oscillators with distributed natural frequencies under the influence of white
noise. The memory patterns are assumed to be given by uniformly distributed
random numbers on so that the patterns encode the phase differences
of the oscillators. To derive the macroscopic order parameter equations for the
network with an extensive number of stored patterns, we introduce the effective
transfer function by assuming the fixed-point equation of the form of the TAP
equation, which describes the time-averaged output as a function of the
effective time-averaged local field. Properties of the networks associated with
synchronization phenomena for a discrete symmetric natural frequency
distribution with three frequency components are studied based on the order
parameter equations, and are shown to be in good agreement with the results of
numerical simulations. Two types of retrieval states are found to occur with
respect to the degree of synchronization, when the size of the width of the
natural frequency distribution is changed.Comment: published in Phys. Rev.
Directed Flow of Information in Chimera States
We investigated interactions within chimera states in a phase oscillator
network with two coupled subpopulations. To quantify interactions within and
between these subpopulations, we estimated the corresponding (delayed) mutual
information that -- in general -- quantifies the capacity or the maximum rate
at which information can be transferred to recover a sender's information at
the receiver with a vanishingly low error probability. After verifying their
equivalence with estimates based on the continuous phase data, we determined
the mutual information using the time points at which the individual phases
passed through their respective Poincar\'{e} sections. This stroboscopic view
on the dynamics may resemble, e.g., neural spike times, that are common
observables in the study of neuronal information transfer. This discretization
also increased processing speed significantly, rendering it particularly
suitable for a fine-grained analysis of the effects of experimental and model
parameters. In our model, the delayed mutual information within each
subpopulation peaked at zero delay, whereas between the subpopulations it was
always maximal at non-zero delay, irrespective of parameter choices. We
observed that the delayed mutual information of the desynchronized
subpopulation preceded the synchronized subpopulation. Put differently, the
oscillators of the desynchronized subpopulation were 'driving' the ones in the
synchronized subpopulation. These findings were also observed when estimating
mutual information of the full phase trajectories. We can thus conclude that
the delayed mutual information of discrete time points allows for inferring a
functional directed flow of information between subpopulations of coupled phase
oscillators
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Adaptive Frequency Neural Networks for Dynamic Pulse and Metre Perception.
Beat induction, the means by which humans listen to music and perceive a steady pulse, is achieved via a perceptualand cognitive process. Computationally modelling this phenomenon is an open problem, especially when processing expressive shaping of the music such as tempo change.To meet this challenge we propose Adaptive Frequency Neural Networks (AFNNs), an extension of Gradient Frequency Neural Networks (GFNNs).GFNNs are based on neurodynamic models and have been applied successfully to a range of difficult music perception problems including those with syncopated and polyrhythmic stimuli. AFNNs extend GFNNs by applying a Hebbian learning rule to the oscillator frequencies. Thus the frequencies in an AFNN adapt to the stimulus through an attraction to local areas of resonance, and allow for a great dimensionality reduction in the network.Where previous work with GFNNs has focused on frequency and amplitude responses, we also consider phase information as critical for pulse perception. Evaluating the time-based output, we find significantly improved re-sponses of AFNNs compared to GFNNs to stimuli with both steady and varying pulse frequencies. This leads us to believe that AFNNs could replace the linear filtering methods commonly used in beat tracking and tempo estimationsystems, and lead to more accurate methods
Semiclassical Phase Reduction Theory for Quantum Synchronization
We develop a general theoretical framework of semiclassical phase reduction
for analyzing synchronization of quantum limit-cycle oscillators. The dynamics
of quantum dissipative systems exhibiting limit-cycle oscillations are reduced
to a simple, one-dimensional classical stochastic differential equation
approximately describing the phase dynamics of the system under the
semiclassical approximation. The density matrix and power spectrum of the
original quantum system can be approximately reconstructed from the reduced
phase equation. The developed framework enables us to analyze synchronization
dynamics of quantum limit-cycle oscillators using the standard methods for
classical limit-cycle oscillators in a quantitative way. As an example, we
analyze synchronization of a quantum van der Pol oscillator under harmonic
driving and squeezing, including the case that the squeezing is strong and the
oscillation is asymmetric. The developed framework provides insights into the
relation between quantum and classical synchronization and will facilitate
systematic analysis and control of quantum nonlinear oscillators.Comment: 20 pages, 5 figure
Delay-induced patterns in a two-dimensional lattice of coupled oscillators
We show how a variety of stable spatio-temporal periodic patterns can be
created in 2D-lattices of coupled oscillators with non-homogeneous coupling
delays. A "hybrid dispersion relation" is introduced, which allows studying the
stability of time-periodic patterns analytically in the limit of large delay.
The results are illustrated using the FitzHugh-Nagumo coupled neurons as well
as coupled limit cycle (Stuart-Landau) oscillators
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