Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results

Synchronization from Disordered Driving Forces in Arrays of Coupled Oscillators

The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We show that random phases in the driving forces result in regular, periodic network behavior. Intermediate phase disorder can produce network synchrony. Specifically, there is an optimal amount of phase disorder, which can induce the highest level of synchrony. These results demonstrate that the spatiotemporal structure of external influences can control chaos and lead to synchronization in nonlinear systems.Comment: 4 pages, 4 figure

The Effect of Different Phases of Synchrony on Pain Threshold in a Drumming Task

Behavioral synchrony has been linked to endorphin activity (Cohen et al., 2010; Sullivan and Rickers, 2013; Sullivan et al., 2014; Tarr et al., 2015, 2016; Weinstein et al., 2016). This has been called the synchrony effect. Synchrony has two dominant phases of movement; in-phase and anti-phase. The majority of research investigating synchrony’s effect on endorphin activity has focused on in-phase synchrony following vigorous activities. The only research to investigate the effects of anti-phase synchrony on endorphin activity found that anti-phase synchronized rowing did not produce the synchrony effect (Sullivan et al., 2014). Anti-phase synchrony, however, is counterintuitive to the sport of rowing and may have interfered with the synchrony effect. This study investigated the effect of anti-phase synchrony on endorphin activity in a different task (i.e., drumming). University students (n D 30) were asked to drum solo and in in-phase and anti-phase pairs for 3 min. Pain threshold was assessed as an indirect indicator of endorphin activity prior to and following the task. Although the in-phase synchrony effect was not found, a repeated measures ANOVA found that there was a significant difference in pain threshold change among the three conditions [F(2,24) D 4.10, ! N2 D 0.255, p < 0.05). Post hoc t-tests showed that the anti-phase condition had a significantly greater pain threshold change than both the solo and in-phase conditions at p < 0.05. This is the first time that anti-phase synchrony has been shown to produce the synchrony effect. Because anti-phase drumming may have required more attention between partners than in-phase synchrony, it may have affected self-other merging (Tarr et al., 2014). These results support Tarr et al.’s (2014) model that multiple mechanisms account for the effect of synchrony on pain threshold, and suggest that different characteristics of the activity may influence the synchrony effect.Brock University Library Open Access Publishing Fun

Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata

Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We show that this phenomenon is a second-order phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics

Dynamics of coupled oscillator systems in presence of a local potential

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective synchronization. We demonstrate by exact results and numerics a surprisingly rich long-time behavior, in which the system settles into either a stationary state that could be in or out of equilibrium and supports either global synchrony or absence of it, or, in a time-periodic synchronized state. The system shows both continuous and discontinuous phase transitions, as well as an interesting reentrant transition in which the system successively loses and gains synchrony on steady increase of the relevant tuning parameter.Comment: v2: close to the published versio