Diversity of dynamical behaviors due to initial conditions: Extension of the Ott-Antonsen ansatz for identical Kuramoto-Sakaguchi phase oscillators.

The Ott-Antonsen ansatz is a powerful tool to extract the behaviors of coupled phase oscillators, but it imposes a strong restriction on the initial condition. Herein, an extension of the Ott-Antonsen ansatz is proposed to relax the restriction, enabling the systematic approximation of the behavior of a globally coupled phase oscillator system with an arbitrary initial condition. The proposed method is validated on the Kuramoto-Sakaguchi model of identical phase oscillators. The method yields cluster and chimera-like solutions that are not obtained by the conventional ansatz.

Asymmetry in cilia configuration induces hydrodynamic phase locking.

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

Temperature-modulated synchronization transition in coupled neuronal oscillators.

We study two firing properties to characterize the activities of a neuron: frequency-current (f-I) curves and phase response curves (PRCs), with variation in the intrinsic temperature scaling parameter (µ) controlling the opening and closing of ionic channels. We show a peak of the firing frequency for small µ in a class I neuron with the I value immediately after the saddle-node bifurcation, which is entirely different from previous experimental reports as well as model studies. The PRC takes a type II form on a logarithmic f-I curve when µ is small. Then, we analyze the synchronization phenomena in a two-neuron network using the phase-reduction method. We find common µ-dependent transition and bifurcation of synchronizations, regardless of the values of I. Such results give us helpful insight into synchronizations tuned with a sinusoidal-wave temperature modulation on neurons.