arXiv subjects

Nariya Uchida

Publications and source records attributed to Nariya Uchida.

At least 19 recordsLinked to original sources

arXiv2026

Optic flow in the visual system determines interaction force and collective motion

Collective motion in animal groups relies on visual cues, yet how individual sensory inputs translate into group-level dynamics remains unclear. Traditional models often assume pre-defined ``3A" rules - avoidance, attraction, and alignment - which require agents to directly access the exact positions and velocities of their neighbors. Here, we propose a minimal model based on fundamental visual processing shared across species: detection of image size and optic flow. We show that the collective patterns, such as vortex and polarized school, emerge spontaneously from the competition between image-size-driven avoidance and optic-flow-driven approach. We find that alignment does not require a pre-assumed velocity-matching rule; instead, it arises from the acceleration of an agent toward regions of strong optic flow. The model shows scale-free velocity correlations and topological visual features observed in animal groups. Our results indicate that the phenomenological 3A forces are not irreducible physical rules, but rather emergent outcomes of basic sensorimotor feedback. This framework provides a physical perspective for linking sensory inputs to macroscopic collective behaviors.

nlin.AO↗

arXiv2026

Noise-driven loss of chimera states and bifurcations in a nonlocal oscillator ring

Independent phase noise can remove the spatial contrast of a chimera while leaving substantial collective coherence. We study this transition in a nonlocally coupled Kuramoto--Sakaguchi ring with a cosine kernel using the nonlinear Fokker--Planck equation. Stationary self-consistency and spatial spectra identify two bifurcations of the uniform ordered state at a reference phase lag. A symmetry-aware amplitude reduction distinguishes a subcritical lower endpoint $D_l$ from a supercritical upper endpoint $D_u$ and shows that reconstruction of the collective rotation frequency is essential to obtain the cubic coefficient. The upper endpoint admits a nonequilibrium Landau-type description of continuous spatial translation-symmetry restoration. Direct integration confirms stationary modulation below the upper threshold, algebraic relaxation at criticality, and exponential decay toward uniform partial synchronization above it. Continuation in noise intensity and phase lag resolves finite-amplitude saddle nodes, a narrow cusp, and a distinct cubic-zero point with a positive quintic coefficient. Together, these results connect the bifurcation structure of noisy chimera branches to spatial symmetry restoration and critical relaxation.

nlin.AO↗

arXiv2026

Heterogeneity-induced chaos in globally coupled Stuart--Landau oscillators

We show that linear-growth-rate heterogeneity combined with complex global coupling can generate quasiperiodicity and chaos in a finite population of Stuart-Landau oscillators with identical natural frequencies and no Kerr-type nonlinear frequency shift. Lyapunov spectra identify limit cycles, quasiperiodic tori, and chaotic attractors, while the order-parameter amplitude exhibits signatures consistent with period-doubling-like transitions towards chaos. We further derive a finite-size invariant manifold of vanishing-order-parameter phase-locked solutions represented by closed polygons with fixed side lengths and demonstrate their configuration-dependent transverse stability. Ensemble sampling reveals pronounced coexistence among polygonal and ordinary phase-locked cycles, quasiperiodic tori, and chaotic attractors. An amplitude-time rescaling identifies the leading parameter approximately organizing the regime boundaries and the similar bifurcation and multistability patterns. These results advance our understanding of collective dynamics in amplitude-inclusive oscillator networks by revealing how heterogeneity and complex coupling jointly shape dynamical complexity, bifurcation structure, and multistability.

nlin.CD↗

arXiv2026

Martingale theory for heat and phase-space contraction in heterogeneous diffusions

We investigate martingale properties of heat dissipated by generic non-equilibrium overdamped Langevin dynamics with multiple dimensions and transport coefficients that may depend explicitly on time and/or space. We find quantitative criteria that establish that heat dissipation may exhibit transient martingale (time-conserved), submartingale (time increasing), and supermartingale (time decreasing) properties in Langevin dynamics with drift coefficients with spatial non-linear dependencies. Furthermore, we reveal a tight link between the heat statistics at stopping (e.g. first-passage) times with that of a functional quantifying the phase-space contraction in the system dynamics. The theoretical results are used to predict the statistical properties of the heat dissipated by a spherical microscopic particle subject to gravity and double-layer forces and hydrodynamically interacting with a rigid wall, whose validity is confirmed by numerical simulations. These results extend the scope of stochastic energetics by revealing a non-trivial relation between heat fluctuations' statistical properties and the non-linear features of non-equilibrium processes.

cond-mat.stat-mech↗

arXiv2026

Wave patterns in two-dimensional networks of non-locally coupled oscillators with phase delay

We studied the wave patterns in non-locally, repulsively coupled oscillators on a 2D lattice. The repulsive coupling is tuned by the phase delay $απ$ and the wave patterns are found in the regime $α\in \left[0.5, 1\right]$. We focused on the growth of orientationally correlated domains and found that the average total boundary size $\overline{|B|}$ obeys an approximate power law $\overline{|B|}\propto t^{-b}$ for $α= 0.8$ and $α=0.9$. In contrast, at $α= 0.7$, the dynamics is disrupted by defect-mediated domain formation and domain splitting. The fitting-window dependence of the apparent exponent $b$, as well as the mean and standard deviation of the wave speed $c$, decreases with increasing $α$, which is consistent with the linear stability analysis of the wave solution.

nlin.PS↗

arXiv2026

Localized inhomogeneity and position-dependent stability of migratory bird formations

We investigate how localized inhomogeneity affects the geometry and stability of migratory bird formations. We use a lifting-line model with a horseshoe-vortex representation to describe the longitudinal dynamics of aerodynamic interactions. As a reference case, we first analyze homogeneous formations and show that their steady states exhibit a U-shaped geometry with hierarchical streamwise spacing, in which adjacent birds become progressively closer toward the leader. We then introduce localized inhomogeneity by modifying the wingspan of a single bird, with its physical properties determined by scaling relations. We determine the range of wingspan variation that preserves a stable formation. The stability range depends strongly on the position of the modified bird, being narrower near the outer wing and broader near the leader. These findings provide a minimal dynamical framework for understanding how local aerodynamic interactions and localized individual differences affect collective flight structures.

nlin.PS↗

arXiv2026

Synchronization and metachronal waves in an array of eukaryotic flagella

We investigate synchronization and metachronal-wave formation in a one-dimensional array of eukaryotic flagella using an elastohydrodynamic model. In contrast to a two-flagellum system, where only in-phase synchronization is stable, larger arrays are found to support stable metachronal waves with finite phase differences. Direct numerical simulations show that metachronal waves appear with increasing probability as the number of flagella increases. To explain this many-body effect, we construct a phase description for the array from that of the pair problem and analyze the stability of phase-locked states with nearest-neighbor hydrodynamic coupling. The analysis shows that increasing system size enlarges the set of stable phase-locked modes, thereby promoting metachronal-wave selection. A continuum description further relates these collective states to advection and diffusion of the phase-difference field. These results provide a simple theoretical framework for understanding how hydrodynamic interactions generate robust metachronal waves in flagellar arrays.

nlin.AO↗

arXiv2026

Dynamical Theory of Elastic Synchronization of Cardiomyocytes

We study synchronization of two cardiomyocytes mediated by elastic interactions through the substrate. Modeling each cell as an oscillating force dipole governed by a Rayleigh-type equation, we derive an effective mechanical coupling from the elastic response of the surrounding medium. Using phase reduction theory, supported by direct numerical simulations, we obtain a dynamical phase description for two cardiomyocytes that predicts geometry-dependent selection of synchronized states. Depending on the mutual orientation, the cells robustly converge to either in-phase or anti-phase beating, yielding an orientation-dependent state map with a nontrivial state boundary. The synchronization time also depends strongly on the distance and mutual orientation of the cells. These results bridge earlier energetic two-body theory and dynamical single-cell theory, and provide a dynamical framework for elastic synchronization of cardiomyocytes.

cond-mat.soft↗

arXiv2026

Defect binding-unbinding transition in active nematic membranes

We investigate the dynamics of active nematic liquid crystals on deformable membranes, focusing on the interplay between active stress and anisotropic curvature coupling. Using a minimal model, we simulate the coupled evolution of the nematic order parameter and membrane height. We demonstrate a continuous transition from a curvature-dominated regime, where topological defects are trapped by local deformation, to an activity-dominated regime exhibiting active turbulence. A scaling analysis reveals that the critical activity threshold $ζ_c$ scales as $α^2/κ$, where $α$ and $κ$ are the coupling constant and bending stiffness, respectively; this relationship is confirmed by our numerical results. Furthermore, we find that significant correlations between the orientational pattern and membrane geometry persist even in the turbulent regime. Specifically, we identify that "walls" in the director field induce characteristic wave-like curvature profiles, providing a mechanism for dynamic coupling between order and shape. These results offer a physical framework for understanding defect-mediated deformation in nonequilibrium biological membranes.

cond-mat.soft↗

arXiv2026

Topological defects in spiral wave chimera states

Chimera states, characterized by the coexistence of coherent and incoherent domains, represent a paradigm of self-organization in complex systems. In this study, we introduce a topological analysis method based on winding numbers to characterize the dynamics of spiral wave chimeras in a two-dimensional phase oscillator network. Our investigation reveals distinct scaling laws governing the system's evolution across the phase lag $α$. Perturbation analysis in the limit $α\to 0$ demonstrates that the incoherent core radius scales linearly with $α$. In contrast, within the stable chimera regime, the average total positive winding number $μ$ follows a clear exponential growth law $μ= ae^{bα}$. This scaling disparity signals a physical crossover from a regime dominated by geometric core expansion to one driven by active topological excitation. Furthermore, we identify a statistical transition in the defect distribution from binomial-like to Poisson-like behavior at a critical threshold $α^*$. These results demonstrate that topological defects possess intrinsic statistical order, establishing $μ$ as a robust macro-variable for analyzing the structural complexity of chimera states.

nlin.AO↗

arXiv2026

Defect states as a precursor of the chimera states in a ring of non-locally coupled oscillators

We investigate the transition from synchronized to chimera states in a ring of non-locally coupled phase oscillators. Our focus is on the intermediate defect states, where solitary waves in the phase gradient profile travel at a constant speed. These traveling defects serve as a dynamical precursor for the nucleation of chimera clusters. The fraction of samples exhibiting defect states increases with the phase delay $α$ and peaks at $α_{c}$, where the system crosses over to asynchronous states filled with chimera clusters. While the traveling speed, number, and width of these defects increase with $α$, the total spatial extent of the defects remains robust against the system size $N$. These results shed new light on the emergence of chimera states in frustrated coupled oscillators.

nlin.AO↗

arXiv2025

Collective behaviors of self-propelled particles with tunable alignment angles

We present a novel aligning active matter model by extending the nematic alignment rule in self-propelled rods to tunable alignment angles, as represented by collision of cone-shaped particles. Non-vanishing alignment angles introduce frustration in the many-body interactions, and we investigate its effect on the collective behavior of the system. Through numerical simulations of an agent-based microscopic model, we found that the system exhibits distinct phenomenology compared to the original self-propelled rods. In particular, anti-parallel bands are observed in an intermediate parameter range. The linear stability analysis of the continuum description derived from the Boltzmann approach demonstrates qualitative consistency with the microscopic model, while frustration due to many-body interactions in the latter destabilizes homogeneous nematic order over a wide range of the alignment angle.

cond-mat.soft↗

arXiv2025

Boltzmann-Ginzburg-Landau theory for autochemotaxis of active rod-like particles

We investigate the interplay between chemotaxis and alignment interactions in active rod-like particles, such as E. coli and Janus rods. Starting from a discrete model of self-propelled rods with chemotactic responses, we employ a Boltzmann-Ginzburg-Landau (BGL) approach to derive coarse-grained dynamical equations for the density, polar and nematic orientational order parameters, and the concentration field of the chemoattractant. We perform a linear stability analysis for fluctuations around uniform steady states corresponding to isotropic and nematic phases. In both phases, we find that translational chemotactic response promotes instability, while rotational chemotactic response suppresses it, elucidating their contrasting effects on the onset of collective dynamics.

cond-mat.soft↗

arXiv2025

Nonreciprocal amplification toward chaos in a chain of Duffing oscillators

A chain of harmonic oscillators with nonreciprocal coupling exhibits characteristic amplification behavior that serves as a classical analog of the non-Hermitian skin effect (NHSE). We extend this concept of nonreciprocal amplification to nonlinear dynamics by employing double-well Duffing oscillators arranged in ring-structured units. The addition of units induces bifurcations of attractors, driving transitions from limit cycles to tori, chaos, and hyper-chaos. Unidirectional couplings between units enable the decomposition of attractors in phase space into projected subspaces corresponding to each unit. In the chaotic regime, amplitude saturation emerges, characterized by monotonically decreasing amplitudes within a unit -- in sharp contrast to} the increasing profiles seen in the linear NHSE. This work uncovers novel bifurcation behavior resulting from the intricate interplay between nonreciprocity and nonlinearity.

nlin.CD↗

arXiv2025

Active nematic liquid crystals under a quenched random field

Coupling between flow and orientation is a central issue in understanding the collective dynamics of active biofilaments and cells. Active stresses generated by motor activity destroy (quasi-)long-range orientational order and induce chaotic flows with many vortices. In cellular and subcellular environment, alignment is also hindered by heterogeneous filamentous structures in extracellular matrix and various intracellular organelles. Here we address the effects of a quenched random field on the flow patterns and orientational order in two-dimensional active nematic liquid crystals. We find that the director dynamics becomes frozen above a critical disorder strength. For sufficiently strong randomness, the orientational correlation function decays exponentially with distance, reproducing the behavior of passive random-field nematics. In contrast, the flow velocity decreases only gradually with increasing disorder, and exhibits a logarithmic spatial correlation under strong randomness. We identify the threshold between the activity- and disorder-dominated regimes and examine its dependence on the activity parameter.

cond-mat.soft↗

arXiv2025

Synchronization of two bacterial flagella as a stochastic process

Synchronization with noise is important for understanding biophysical processes at nano- and micro-meter scales, such as neuronal firing and flagellar rotations. To understand the energetics of these processes, stochastic thermodynamics approaches are useful. Due to large fluctuations in a small system, ensemble averages of thermodynamic quantities are not sufficient to characterize the energetics of an individual sample. In this paper, we use a model for synchronization of bacterial flagella as an example, and develop an approximation method for analyzing the phase and heat dissipation in trajectories for different noise realizations. We describe the {temporal evolution} of the phase difference and heat dissipation as stochastic processes, and verify the analytical results by numerical simulations.

nlin.AO↗

arXiv2025

Boltzmann approach to collective motion via nonlocal visual interaction

Visual cues play crucial roles in the collective motion of animals, birds, fish, and insects. The interaction mediated by visual information is essentially non-local and has many-body nature due to occlusion, which poses a challenging problem in modeling the emergent collective behavior. In this paper, we introduce a Boltzmann-equation approach incorporating non-local visual interaction. Occlusion is treated in a self-consistent manner via a coarse-grained density field, which renders the interaction effectively pairwise. Our model also incorporates the recent finding that each organism stochastically selects a neighbor to interact at each instant. We analytically derive the order-disorder transition point, and show that the visual screening effect raises the transition threshold, which does not vanish when the density of the agents or the range of the intrinsic interaction is taken to infinity. Our analysis suggests that the model exhibits a discontinuous transition as in the local interaction models, and but the discontinuity is weakened by the non-locality. Our study clarifies the essential role of non-locality in the visual interactions among moving organisms.

nlin.AO↗

arXiv2024

Metastability of multi-population Kuramoto-Sakaguchi oscillators

An Ott-Antonsen reduced $M$-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter $α$ on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability. Linear stability analysis reveals the stable regions of coherent states with different winding numbers $q$. Within certain $α$ ranges, the system settles into stable traveling wave solutions despite the coherent states also being linearly stable. For around $α\approx 0.46π$, the system displays the most frequent metastable transitions between coherent states and partially synchronized states, while for $α$ closer to $π/2$, metastable transitions arise between partially synchronized states and modulated states. This model captures metastable dynamics akin to brain activity, offering insights into the synchronization of brain networks.

nlin.AO↗