arXiv subjects

Tae-Wook Ko

Publications and source records attributed to Tae-Wook Ko.

9 recordsLinked to original sources

arXiv2026

Common Noise-Induced Group-Level Synchronization Between Uncoupled Groups of Oscillators

We investigate group-level synchronization between oscillator groups induced by common noise in the absence of inter-group coupling. Each group receives a common noise shared by all its oscillators and independent local noise inputs to individual oscillators. The same common noise is applied to all groups. The system is studied with both identical and nonidentical oscillators, and with and without intra-group coupling. In the nonidentical case, natural frequencies are drawn from the same distribution for both groups, making them statistically equivalent. Through numerical simulations of this system, we find that the degree of synchronization within each group, measured by the absolute value of a complex Kuramoto order parameter, typically shows significant temporal fluctuations. Importantly, the complex order parameters representing the collective oscillations of the groups synchronize when the groups are driven by the same common noise. By deriving a phase density evolution mapping, we analytically explain how this group-level synchronization is achieved in the absence of intra-group coupling.

nlin.AO↗

arXiv2024

Hysteresis in a Generalized Kuramoto Model with a Simplified Realistic Coupling Function and Inhomogeneous Coupling Strengths

We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a simplified, more realistic coupling function. With the more realistic coupling function and the coupling strength inhomogeneity, each oscillator acquires an effective intrinsic frequency proportional to its individual coupling strength. This is analogous to the positive coupling strength-frequency correlation introduced explicitly or implicitly in some previous models with nonidentical oscillators that show explosive synchronization and hysteresis. Through numerical simulations and analysis using truncated Gaussian, uniform, and truncated power-law coupling strength distributions, we observe that the system can exhibit abrupt phase transitions and hysteresis. The distribution of coupling strengths significantly affects the hysteresis regions within the parameter space of the coupling function. Additionally, numerical simulations of models with weighted networks including a brain network confirm the existence of hysteresis due to the realistic coupling function and coupling strength inhomogeneity, suggesting the broad applicability of our findings to complex real-world systems.

math.DS↗

arXiv2008

Phase Response Curves of Coupled Oscillators

Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.

q-bio.NC↗

arXiv2008

Partially Locked States in Coupled Oscillators due to Inhomogeneous Coupling

We investigate coupled identical phase oscillators with scale-free distribution of coupling strength. It is shown that partially locked states can occur due to the inhomogeneity in coupling and some properties of the coupling function. Various quantities of the partially locked states are computed through a self-consistency argument and the values show good agreement with simulation results.

nlin.AO↗

arXiv2007

Emergence of Chaotic Itinerancy in Simple Ecological Systems

Chaotic itinerancy is a universal dynamical concept that describes itinerant motion among many different ordered states through chaotic transition in dynamical systems. Unlike the expectation of the prevalence of chaotic itinerancy in high-dimensional systems, we identify chaotic itinerant behavior from a relatively simple ecological system, which consists only of two coupled consumer-resource pairs. The system exhibits chaotic bursting activity, in which the explosion and the shrinkage of the population alternate indefinitely, while the explosion of one pair co-occurs with the shrinkage of the other pair. We analyze successfully the bursting activity in the framework of chaotic itinerancy, and find that large duration times of bursts tend to cluster in time, allowing the effective burst prognosis. We also investigate the control schemes on the bursting activity, and demonstrate that invoking the competitive rise of the consumer in one pair can even elongate the burst of the other pair rather than shorten it.

nlin.CD↗

arXiv2005

Pattern Formation in a Two-Dimensional Array of Oscillators with Phase-Shifted Coupling

We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike pinwheels, (anti)spirals with phase-randomized cores, and antiferro patterns embedded in (anti)spirals. We consider the symmetry properties of the system to explain the observed behaviors, and estimate the wavelengths of the patterns by linear analysis. Finally, we point out the implications of our work for biological neural networks.

nlin.PS↗

arXiv2002

Time-delayed Spatial Patterns in a Two-dimensional Array of Coupled Oscillators

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control parameter in this study. It is found that distance-dependent time-delays induce various patterns including traveling rolls, square-like and rhombus-like patterns, spirals, and targets. We analyzed the stability boundaries of the emerging patterns and briefly pointed out the possible empirical implications of such time-delayed patterns.

nlin.PS↗

arXiv2001

Hexagon Formation as a Compromise Between Squares and Stripes in Vertically Vibrated Granular Layers

We propose a spatially continuous and temporally discrete model for pattern formation in vertically vibrated granular layers. The grain transfer and the grain mobility transitions are introduced qualitatively, but explicitly. This model reproduces experimentally observed f/2 patterns, including squares in high-mobility conditions and stripes in low-mobility conditions. Hexagons are obtained when a high-mobility condition and a low-mobility condition are alternately applied. We discuss this hexagon formation in connection with the formation of squares and stripes. In addition to the experimentally observed localized oscillon structures, this model also exhibits localized hexagonal structures. These localized hexagonal structures grow by nucleating oscillons of equal phase.

nlin.PS↗

arXiv2000

Nearest pattern interaction and global pattern formation

We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration.

nlin.PS↗