arXiv subjects

Peter V. E. McClintock

Publications and source records attributed to Peter V. E. McClintock.

22 records · Page 2Linked to original sources

arXiv2008

Interplay between couplings and common noise in phase synchronization: disagreement between global analysis and local stability characterization

We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the "effective coupling" is big compared to the common noises, the former favors and the latter hinder synchronization. On the contrary, when the coupling is small compared to the proportional noises, we find that the latter induce synchronization, optimally when their intensities are big and in the n:m synchronization ratio. Furthermore, in such case a small value of the coupling is better for synchronization. Finally, we show that synchronization, which is a global property, must not be studied via local stability such as with Lyapunov exponents.

nlin.SI↗

arXiv2008

High-order synchronization, transitions, and competition among Arnold tongues in a rotator under harmonic forcing

We consider a rotator whose equation of motion for the angle $θ$ consists of the zeroth and first Fourier modes. Numerical analysis based on the trailing of saddle-node bifurcations is used to locate the n:1 Arnold tongues where synchronization occurs. Several of them are wide enough for high-order synchronization to be seen in passive observations. By sweeping the system parameters within a certain range, we find that the stronger the dependence of $\dotθ$ on $θ$, the wider the regions of synchronization. Use of a synchronization index reveals a vast number of very narrow n:m Arnold tongues. A competition phenomenon among the tongues is observed, in that they "push" and "squeeze" one another: as some tongues widen, others narrow. Two mechanisms for transitions between different n:m synchronization states are considered: slow variation of the driving frequency, and the influence of low-frequency noise on the rotator.

nlin.CD↗

arXiv2008

Neuronal synchrony during anaesthesia - A thalamocortical model

There is growing evidence in favour of the temporal-coding hypothesis that temporal correlation of neuronal discharges may serve to bind distributed neuronal activity into unique representations and, in particular, that $θ$ (3.5-7.5 Hz) and $δ$ ($0.5<$3.5 Hz) oscillations facilitate information coding. The $θ$ and $δ$ rhythms are shown to be involved in various sleep stages, and during anæsthesia, and they undergo changes with the depth of anæsthesia. We introduce a thalamocortical model of interacting neuronal ensembles to describe phase relationships between $θ$ and $δ$ oscillations, especially during deep and light anæsthesia. Asymmetric and long range interactions among the thalamocortical neuronal oscillators are taken into account. The model results are compared with the experimental observations of Musizza et al. {\it J. Physiol. (London)} 2007 580:315-326. The $δ$ and $θ$ activities are found to be separately generated and are governed by the thalamus and cortex respectively. Changes in the degree of intra--ensemble and inter--ensemble synchrony imply that the neuronal ensembles inhibit information coding during deep anæsthesia and facilitate it during light anæsthesia.

q-bio.NC↗

arXiv2008

Routes to synchrony between asymmetrically interacting oscillator ensembles

We report that asymmetrically interacting ensembles of oscillators (AIEOs) follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurrence of the routes is determined by phase asymmetry. The identification of these phenomena offers new insight into synchrony between oscillator ensembles and suggest new ways in which it may be controlled.

nlin.PS↗