192 research outputs found
Synchronization of weakly perturbed Markov chain oscillators
Rate processes are simple and analytically tractable models for many
dynamical systems which switch stochastically between a discrete set of quasi
stationary states but they may also approximate continuous processes by coarse
grained, symbolic dynamics. In contrast to limit cycle oscillators which are
weakly perturbed by noise, the stochasticity in such systems may be strong and
more complicated system topologies than the circle can be considered. Here we
employ second order, time dependent perturbation theory to derive expressions
for the mean frequency and phase diffusion constant of discrete state
oscillators coupled or driven through weakly time dependent transition rates.
We also describe a method of global control to optimize the response of the
mean frequency in complex transition networks.Comment: 16 pages, 7 figure
Collective Phase Sensitivity
The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.Comment: 6 pages, 3 figure
Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback
A theoretical framework is developed for a precise control of spatial
patterns in oscillatory media using nonlinear global feedback, where a proper
form of the feedback function corresponding to a specific pattern is predicted
through the analysis of a phase diffusion equation with global coupling. In
particular, feedback functions that generate the following spatial patterns are
analytically given: i) 2-cluster states with an arbitrary population ratio, ii)
equally populated multi-cluster states, and iii) a desynchronized state. Our
method is demonstrated numerically by using the Brusselator model in the
oscillatory regime. Experimental realization is also discussed.Comment: 18 pages, 4 figures, accepted in New Journal of Physic
Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
We study a large population of globally coupled phase oscillators subject to
common white Gaussian noise and find analytically that the critical coupling
strength between oscillators for synchronization transition decreases with an
increase in the intensity of common noise. Thus, common noise promotes the
onset of synchronization. Our prediction is confirmed by numerical simulations
of the phase oscillators as well as of limit-cycle oscillators
Collective dynamical response of coupled oscillators with any network structure
We formulate a reduction theory that describes the response of an oscillator
network as a whole to external forcing applied nonuniformly to its constituent
oscillators. The phase description of multiple oscillator networks coupled
weakly is also developed. General formulae for the collective phase sensitivity
and the effective phase coupling between the oscillator networks are found. Our
theory is applicable to a wide variety of oscillator networks undergoing
frequency synchronization. Any network structure can systematically be treated.
A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure
Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling
The phenomenon of slow switching in populations of globally coupled
oscillators is discussed. This characteristic collective dynamics, which was
first discovered in a particular class of the phase oscillator model, is a
result of the formation of a heteroclinic loop connecting a pair of clustered
states of the population. We argue that the same behavior can arise in a wider
class of oscillator models with the amplitude degree of freedom. We also argue
how such heteroclinic loops arise inevitably and persist robustly in a
homogeneous population of globally coupled oscillators. Although the
heteroclinic loop might seem to arise only exceptionally, we find that it
appears rather easily by introducing the time-delay in the population which
would otherwise exhibit perfect phase synchrony. We argue that the appearance
of the heteroclinic loop induced by the delayed coupling is then characterized
by transcritical and saddle-node bifurcations. Slow switching arises when the
system with a heteroclinic loop is weakly perturbed. This will be demonstrated
with a vector model by applying weak noises. Other types of weak
symmetry-breaking perturbations can also cause slow switching.Comment: 10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev.
Establishment of the Standard Prophylactic Strategy for Peritoneal Recurrence and Proposal of the Optimal Therapeutic Protocol for Gastric Cancer
A Proposal of a Practical and Optimal Prophylactic Strategy for Peritoneal Recurrence
Peritoneal metastasis, which often arises in patients with advanced gastric cancer, is well known as a miserable and ill-fated disease. Once peritoneal metastasis is formed, it is extremely difficult to defeat. We advocated EIPL (extensive intraoperative peritoneal lavage) as a useful and practical adjuvant surgical technique for those gastric cancer patients who are likely to suffer from peritoneal recurrence. In this paper, we review the effect of EIPL therapy on prevention of peritoneal recurrence on patients with peritoneal free cancer cells without overt peritoneal metastasis (CY+/P−) through the prospective randomized study, and we verified its potential as an optimal and standard prophylactic therapeutic strategy for peritoneal recurrence
- …