19 research outputs found
Acceleration effect of coupled oscillator systems
We have developed a curved isochron clock (CIC) by modifying the radial
isochron clock to provide a clean example of the acceleration (deceleration)
effect. By analyzing a two-body system of coupled CICs, we determined that an
unbalanced mutual interaction caused by curved isochron sets is the minimum
mechanism needed for generating the acceleration (deceleration) effect in
coupled oscillator systems. From this we can see that the Sakaguchi and
Kuramoto (SK) model which is a class of non-frustrated mean feild model has an
acceleration (deceleration) effect mechanism. To study frustrated coupled
oscillator systems, we extended the SK model to two oscillator associative
memory models, one with symmetric and one with asymmetric dilution of coupling,
which also have the minimum mechanism of the acceleration (deceleration)
effect. We theoretically found that the {\it Onsager reaction term} (ORT),
which is unique to frustrated systems, plays an important role in the
acceleration (de! celeration) effect. These two models are ideal for evaluating
the effect of the ORT because, with the exception of the ORT, they have the
same order parameter equations. We found that the two models have identical
macroscopic properties, except for the acceleration effect caused by the ORT.
By comparing the results of the two models, we can extract the effect of the
ORT from only the rotation speeds of the oscillators.Comment: 35 pages, 10 figure
Phase Transitions of an Oscillator Neural Network with a Standard Hebb Learning Rule
Studies have been made on the phase transition phenomena of an oscillator
network model based on a standard Hebb learning rule like the Hopfield model.
The relative phase informations---the in-phase and anti-phase, can be embedded
in the network. By self-consistent signal-to-noise analysis (SCSNA), it was
found that the storage capacity is given by , which is better
than that of Cook's model. However, the retrieval quality is worse. In
addition, an investigation was made into an acceleration effect caused by
asymmetry of the phase dynamics. Finally, it was numerically shown that the
storage capacity can be improved by modifying the shape of the coupling
function.Comment: 10 pages, 6 figure
An associative memory of Hodgkin-Huxley neuron networks with Willshaw-type synaptic couplings
An associative memory has been discussed of neural networks consisting of
spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which
memorize P patterns in their synaptic weights. In addition to excitatory
synapses whose strengths are modified after the Willshaw-type learning rule
with the 0/1 code for quiescent/active states, the network includes uniform
inhibitory synapses which are introduced to reduce cross-talk noises. Our
simulations of the HH neuron network for the noise-free state have shown to
yield a fairly good performance with the storage capacity of for the low neuron activity of . This
storage capacity of our temporal-code network is comparable to that of the
rate-code model with the Willshaw-type synapses. Our HH neuron network is
realized not to be vulnerable to the distribution of time delays in couplings.
The variability of interspace interval (ISI) of output spike trains in the
process of retrieving stored patterns is also discussed.Comment: 15 pages, 3 figures, changed Titl
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.