285 research outputs found
Quantum correlations and synchronization measures
The phenomenon of spontaneous synchronization is universal and only recently
advances have been made in the quantum domain. Being synchronization a kind of
temporal correlation among systems, it is interesting to understand its
connection with other measures of quantum correlations. We review here what is
known in the field, putting emphasis on measures and indicators of
synchronization which have been proposed in the literature, and comparing their
validity for different dynamical systems, highlighting when they give similar
insights and when they seem to fail.Comment: book chapter, 18 pages, 7 figures, Fanchini F., Soares Pinto D.,
Adesso G. (eds) Lectures on General Quantum Correlations and their
Applications. Quantum Science and Technology. Springer (2017
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
We present a detailed study of the effect of time delay on the collective
dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple
model consisting of just two oscillators with a time delayed coupling, the
bifurcation diagram obtained by numerical and analytical solutions shows
significant changes in the stability boundaries of the amplitude death, phase
locked and incoherent regions. A novel result is the occurrence of amplitude
death even in the absence of a frequency mismatch between the two oscillators.
Similar results are obtained for an array of N oscillators with a delayed mean
field coupling and the regions of such amplitude death in the parameter space
of the coupling strength and time delay are quantified. Some general analytic
results for the N tending to infinity (thermodynamic) limit are also obtained
and the implications of the time delay effects for physical applications are
discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor
changes over the previous version; To be published in Physica
Optimal Subharmonic Entrainment
For many natural and engineered systems, a central function or design goal is
the synchronization of one or more rhythmic or oscillating processes to an
external forcing signal, which may be periodic on a different time-scale from
the actuated process. Such subharmonic synchrony, which is dynamically
established when N control cycles occur for every M cycles of a forced
oscillator, is referred to as N:M entrainment. In many applications,
entrainment must be established in an optimal manner, for example by minimizing
control energy or the transient time to phase locking. We present a theory for
deriving inputs that establish subharmonic N:M entrainment of general nonlinear
oscillators, or of collections of rhythmic dynamical units, while optimizing
such objectives. Ordinary differential equation models of oscillating systems
are reduced to phase variable representations, each of which consists of a
natural frequency and phase response curve. Formal averaging and the calculus
of variations are then applied to such reduced models in order to derive
optimal subharmonic entrainment waveforms. The optimal entrainment of a
canonical model for a spiking neuron is used to illustrate this approach, which
is readily extended to arbitrary oscillating systems
Dynamic synchronization of sympathetic oscillators
Synchronous activity of single postganglionic sympathetic neurones (PGNs) underlies rhythmical or semi-rhythmical burst discharges recorded from peripheral sympathetic nerves. It is still controversial whether this rhythmicity is generated by an autonomous sympathetic oscillator. Previous studies have demonstrated that activity of single PGNs innervating the caudal ventral artery (CVA) of the rat's tail has a dominant rhythm (T-rhythm). The frequency of T- rhythm is different from the cardiac frequency and can be different from those of ventilatory and respiratory rhythms, suggesting that T-rhythm is generated by an oscillator independent of periodic drives originating from the arterial baroreceptors, the ventilation afferents and the respiratory network. Using the rat's tail circulation as a model, the purpose of the present study is: 1) to determine whether activity from different single PGNs is generated by multiple oscillators. 2) to establish whether synchronization of single PGNs is an obligatory feature and if not, how it is regulated. 3) to determine whether periodically driven single PGN oscillators exhibit dynamics as predicted by the theory of nonlinear coupled oscillators. 4) to explain the discharge behaviour of whole nerve activity based on the findings at single PGN level.
The experiments were conducted in anaesthetized Sprague-Dawley rats. Population PGN activity was recorded from the ventral collector nerve (VCN) of the tail. Single PGN activity was recorded focally from the surface of the CVA. The interaction between two single PGNs was studied by recording two units simultaneously. The discharge behaviours of PGNs in response to a periodic input were studied using the central respiratory drive (CRD) and lung-inflation cycle (LlC)-related activity as the driving forces.
The findings from the present study suggest that: 1) Activity of CVA PGNs is generated by multiple oscillators independent of CRD, LIC-related activity and cardiac activity. 2) The multiple PGN oscillators are capable of dynamic synchronization. 3) When subjected to frequency changes of LICs, single PGNs exhibit dynamics, such as 1:1 entrainment, relative coordination, high order rational frequency-lock, asynchrony, characterising nonlinear coupled oscillators. 4) Population PGN activity should be considered as output activity from a pool of dynamically interactive multiple oscillators rather than that from a single oscillator
Entrainment in forced Winfree systems
Rhythmic behavior is widely present in living organisms. The rhythms can be innate and usually they are externally stimulated by the environment. One such stimulus is the 24 h natural light-dark cycle which governs the activity-inactivity cycle of many plants, animals and humans. The cells in the suprachiasmatic nucleus that govern our circadian rhythms are ideally regarded as a group of biological oscillators. In the Winfree model, the biological oscillators are regarded as coupled oscillators. The Winfree model was used to describe the synchronization of a large system of globally coupled phase oscillators. Considering that external stimuli and environmental factors, such as the change of light and darkness, have great influence on the rhythmic behavior, a periodic forcing is added to Winfree system. The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of non-identical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The Ott-Antonsen is used to give a low-dimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and non-detuned cases for identical oscillators and understand the entrainment patterns using stability theory
Linear response theory for coupled phase oscillators with general coupling functions
We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is applicable to a wide class of coupled phase oscillator systems and allows for any coupling functions, any natural frequency distributions, any phase-lag parameters, and any values for the time-delay parameter. This generality is in contrast to the limitation of the previous methods of the Ott–Antonsen ansatz and the self-consistent equation for an order parameter, which are restricted to a model family whose coupling function consists of only a single sinusoidal function. The theory is verified by numerical simulations
Detection of synchronization from univariate data using wavelet transform
A method is proposed for detecting from univariate data the presence of
synchronization of a self-sustained oscillator by external driving with varying
frequency. The method is based on the analysis of difference between the
oscillator instantaneous phases calculated using continuous wavelet transform
at time moments shifted by a certain constant value relative to each other. We
apply our method to a driven asymmetric van der Pol oscillator, experimental
data from a driven electronic oscillator with delayed feedback and human
heartbeat time series. In the latest case, the analysis of the heart rate
variability data reveals synchronous regimes between the respiration and slow
oscillations in blood pressure.Comment: 10 pages, 9 figure
A study of poststenotic shear layer instabilities
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