Persistent fluctuations in synchronization rate in globally coupled oscillators with periodic external forcing

Implementation and Long-Term Evaluation of a Hearing Aid Supported Tinnitus Treatment Using Notched Environmental Sounds

Recent work has shown that sharp spectral edges in acoustic stimuli might have advantageous effects in the treatment of tonal tinnitus. In the course of this paper, we evaluate the long-term effects of spectrally notched hearing aids on the subjective tinnitus distress. By merging recent experimental work with a computational tinnitus model, we modified the commercially available behind-the-ear hearing aids so that a frequency band of 0.5 octaves, centered on the patient’s individual tinnitus frequency, was blocked out. Those hearing aids employ a steep notch filter that filters environmental sounds to suppress the tinnitus-related changes in neural firing by lateral inhibition. The computational model reveals a renormalization of pathologically increased neural response reliability and synchrony in response to spectrally modified input. The target group, fitted with spectrally notched hearing aids, was matched with a comparable control group, fitted with standard hearing aids of the same type but without a notch filter. We analyze the subjective self-assessment by tinnitus questionnaires, and we monitor the objective distress correlates in auditory evoked response phase data. Both, subjective and objective results show a noticeable trend of a larger therapeutic benefit for notched hearing correction.

Nonautonomous driving induces stability in network of identical oscillators

Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous perturbation is a good candidate for stabilizing complex dynamics, we consider a network of identical phase oscillators driven by an oscillator with a slowly time-varying frequency. We investigate both the short- and long-term stability of the synchronous solutions of this nonautonomous system. For attractive couplings we show that the region of stability grows as the amplitude of the frequency modulation is increased, through the birth of an intermittent synchronization regime. For repulsive couplings, we propose a control strategy to stabilize the dynamics by altering very slightly the network topology. We also show how, without changing the topology, time-variability in the driving frequency can itself stabilize the dynamics. As a byproduct of the analysis, we observe chimeralike states. We conclude that time-variability-induced stability phenomena are also present in networks, reinforcing the idea that this is a quite realistic scenario for living systems to use in maintaining their functioning in the face of ongoing perturbations.

Symmetry and symmetry breaking in a Kuramoto model induced on a Möbius strip

The concept of bounded confidence in social dynamics is introduced into the Kuramoto model. Then a model with projective symmetry is naturally induced by a principal Z(2) bundle over a circle. A Möbius strip is constructed as the manifold of interactions such that two "sides" of a local section correspond to antipodal couplings with opposite signs. We show analytically that symmetric polarization of synchronized states (conformist vs contrarian) can emerge from the collective behavior of homogeneously coupled oscillators. In the continuum limit, a generalized asymmetric model reverts to the symmetric case under uniform initial condition, whereas for networks of finite size, it exhibits richer dynamics or the ordinary behavior of the classic model via symmetry breaking, depending on the relevant parameters values. The symmetry and symmetry breaking of the synchronization state are analogous to the concepts of equality and majority of opinions in sociophysical models of opinion formation. The synchronized clusters can be one (consensus), two (polarization), or more (fragmentation), as opinion clusters.

Periodicity suppression in continuous-time dynamical systems by external forcing

We investigate periodicity suppression by an external periodic forcing in different flows, each modeled by a set of three autonomous nonlinear first-order ordinary differential equations. By varying the amplitude of a sinusoidal forcing with a fixed angular frequency, we show through numerical simulations, including parameter planes plots, phase-space portraits, and the largest Lyapunov exponent, that windows of periodicity embedded in chaotic regions may be totally suppressed.