arXiv subjects

Yuta Tateyama

Publications and source records attributed to Yuta Tateyama.

3 recordsLinked to original sources

arXiv2026

Continuum mean-field theory of spatiotemporal pattern formation in a three-state active Potts model

We investigate the spatiotemporal dynamics of a three-state active Potts model with a cyclic transition bias. Starting from microscopic Glauber-type dynamics, we derive macroscopic continuum field equations through a spatial mean-field approximation. Linear stability and weakly nonlinear analyses reveal that increasing the coupling strength induces a Hopf bifurcation, near which the critical amplitude dynamics is described by the complex Ginzburg--Landau equation. In the spatially homogeneous limit, the system exhibits limit-cycle oscillations and ordered states, with an intermediate regime of bistability bounded by a $\mathbb{Z}_3$-symmetric heteroclinic bifurcation. In two dimensions, the system sustains stable rotating spiral waves. Using perturbation theory based on one-dimensional traveling fronts, we semianalytically predict the curvature-dependent propagation velocity of circular fronts, as well as the rotational angular velocity and pitch of spiral waves. Finally, we compare the continuum model with discrete Monte Carlo simulations to clarify the role of thermal fluctuations and evaluate the validity of the mean-field approximation.

nlin.PS↗

arXiv2026

Higher-codimension points as organizing centers in nonreciprocal pattern-forming systems with O(2)-symmetry

Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady and dynamic phases. Complementing the numerical analysis of the field equations with time simulations and path continuation techniques, we derive a reduced dynamical system corresponding to a one-mode approximation for the critical-wavenumber modes. Furthermore, we derive the normal form equations that are valid in the vicinity of the Takens-Bogdanov bifurcation with O(2)-symmetry, which allows us to draw on corresponding literature results. Comparing results obtained on the different levels of description, we discuss the bifurcation structure relating trivial uniform and inhomogeneous steady states as well as traveling, standing and modulated waves. We also contextualize the relevance of recently highlighted features of the linear mode structure, i.e., of the dispersion relations, termed "critical exceptional points" for the transitions between the nonequilibrium phases.

nlin.PS↗

arXiv2024

Pattern dynamics of the nonreciprocal Swift-Hohenberg model

We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We classify the characteristic spatiotemporal patterns obtained in numerical simulation by focusing on the spatiotemporal Fourier spectrum of the order parameters. We derive a reduced dynamical system by using the spatial Fourier series expansion. We analyze the bifurcation structure around the fixed points corresponding to the aligned and chiral phases, and explain the transitions between them. The disordered phase is destabilized either to the aligned phase by the Turing bifurcation or to the chiral phase by the wave bifurcation, while the aligned phase and the chiral phase are connected by the pitchfork bifurcation.

nlin.PS↗