Characterizing the phase synchronization transition of chaotic oscillators

Phase locking route behind complex periodic windows in a forced oscillator

Chaotic systems have complex reactions against an external driving force; even in cases with low-dimension oscillators, the routes to synchronization are diverse. We proposed a stroboscope-based method for analyzing driven chaotic systems in their phase space. According to two statistic quantities generated from time series, we could realize the system state and the driving behavior simultaneously. We demonstrated our method in a driven bi-stable system, which showed complex period windows under a proper driving force. With increasing periodic driving force, a route from interior periodic oscillation to phase synchronization through the chaos state could be found. Periodic windows could also be identified and the circumstances under which they occurred distinguished. Statistical results were supported by conditional Lyapunov exponent analysis to show the power in analyzing the unknown time series.

Information flow in heterogeneously interacting systems

Motivated by studies on the dynamics of heterogeneously interacting systems in neocortical neural networks, we studied heterogeneously-coupled chaotic systems. We used information-theoretic measures to investigate directions of information flow in heterogeneously coupled Rössler systems, which we selected as a typical chaotic system. In bi-directionally coupled systems, spontaneous and irregular switchings of the phase difference between two chaotic oscillators were observed. The direction of information transmission spontaneously switched in an intermittent manner, depending on the phase difference between the two systems. When two further oscillatory inputs are added to the coupled systems, this system dynamically selects one of the two inputs by synchronizing, selection depending on the internal phase differences between the two systems. These results indicate that the effective direction of information transmission dynamically changes, induced by a switching of phase differences between the two systems.

Detection of diffusion anisotropy due to particle asymmetry from single-particle tracking of Brownian motion by the large-deviation principle

We show that the diffusion anisotropy due to the asymmetry of the particle can be extracted from the trajectory data without the information of the particle orientation. The subject of analysis is typical in single-particle tracking (SPT) experiments, and the analysis is based on the large-deviation principle in mathematics. We consider the model system of Langevin equations in two dimensions where a particle diffusion shows anisotropy depending on a single parameter defined by the two diffusion coefficients in the perpendicular directions of the frame fixed to the particle. We show how the large-deviation quantities depend on this parameter so that it can be used for the detection of the diffusion anisotropy. We also illustrate how the discreteness of the sampling interval in the SPT and the finiteness of the number of samples influence the results of the analysis.