Chaos最新文献

We investigate the dynamics of a solitary wave in the nonlinear Dirac equation under a spatially periodic potential with wave number k. Using a two-collective-coordinate ansatz, we derive an effective equation of motion for the solitary wave's center of mass based on energy conservation and on momentum continuity equation with a source term. The solitary wave behaves as a relativistic particle in an effective potential, which in the non-relativistic limit reduces to a nonlinear pendulum in a sinusoidal potential of period λ = 2π/k. The dynamics is governed by the interplay between the potential period λ and the solitary wave width Ls. The wave number k controls both the period and amplitude of the effective potential, leading to distinct regimes. For λ ≫ Ls, the solitary wave exhibits either bounded oscillations or unbounded motion, depending on its initial velocity; in contrast, for λ ≪ Ls, the potential amplitude is effectively negligible and the motion becomes uniform. In the particle-like regime, a critical initial velocity separates trapped and unbounded motion. At low frequencies, where the solitary wave develops a two-hump structure, we observe a λ/2 phase shift in the effective potential and the conversion of energy associated with internal shape oscillations into translational kinetic energy, a mechanism that lies beyond the point-particle description and reveals behavior not typically associated with length-scale competition in solitary wave systems.

Models of cardiac tissue span a wide range of complexity, from minimal models to biophysically detailed models. It is often assumed that minimal models accurately capture the core behaviors of propagating action potentials in biophysically detailed models. However, it remains unclear whether additional physiological detail introduces qualitatively new behaviors. Dispersion relations quantify the existence, stability, and bifurcations of traveling waves, but their computation for biophysically detailed models has been limited by system complexity and computational cost. To overcome these challenges, we develop Traveling Wave Investigation Software Tool (TWIST), a numerical framework for the systematic computation of traveling wave solutions and their spectra. Using TWIST, we compute and compare dispersion relations in the FitzHugh-Nagumo, Beeler-Reuter, and nine-variable ten Tusscher-Panfilov models. Our analysis shows that increasing physiological detail can introduce substantial additional structure in dispersion relations. In particular, the interaction of multiple activation processes in the ten Tusscher-Panfilov model gives rise to additional solution branches, including families of slow waves that are absent in minimal models and may play important roles in abnormal wave dynamics. Our comparisons across models of increasing complexity distinguish robust features of wave propagation from those arising specifically from detailed ionic interactions and represent a step toward validating that the observed behaviors reflect genuine cardiac phenomena rather than artifacts of specific model formulations.

As is well known, there have been extensive studies on the bifurcation of limit cycles for near-Hamiltonian systems. In this paper, we provide a new method to produce limit cycles near a class of heteroclinic loops with two or three saddles. More precisely, we perturb the polycycle to form a perturbed 2-polycycle and then produce limit cycles by changing the stability of the perturbed 2-polycycle. We also present two examples as applications, which demonstrate the advantages of our new method.

This paper uses a network model to analyze the impact of the COVID-19 pandemic on global trade centers. Using import-export trade data from 12 major economies, we visually assess the shifts in global trade network positions before and after the pandemic. By constructing a balanced trade network for the years 2018, 2019, and 2020, we examine how the pandemic has affected the trade connections of key countries. Our study finds that China maintained positive growth and strengthened its trade ties with the United States, while other major economies experienced declines in their network positions. Subsequently, we apply Liang-Kleeman Information Flow to conduct a causal analysis of the past 30 years of gross domestic product and trade data between China and the United States, demonstrating how economic growth patterns influence changes in the global trade network. This combination of network analysis and causal inference provides robust support for our conclusions on the evolving structure of global trade centers.

Coherence resonance characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we investigate the stochastic dynamics of a 3D Sherman-Rinzel-Keizer model driven by multiplicative Feller noise. We show that traditional extremal evaluations of coherence resonance encounter a bathtub effect, characterized by a broad resonance valley, which can lead to statistical inaccuracies. To address this, we propose a logarithmic centroid extraction method, which filters out stochastic jitter and recovers the underlying adiabatic Kramers scaling with high linearity (R2 > 0.95). Furthermore, we identify the physical boundary where this adiabatic approximation breaks down under the strong-noise limit. Extending our analysis to gap-junction coupled systems, we observe a noise-induced transition from sub-threshold physiological shivering (characterized by statistical correlation but negligible functional output) to macroscopic functional synchronization. Our results provide a mathematical framework for extracting optimal noise intensities in broad energy valleys and offer insights into how quiescent biological systems utilize stochastic fluctuations for functional recovery.

Inferring the dynamics of infectious diseases enables prediction and intervention. During early monitoring, available information may comprise digital contact data that partly resolve the interaction network and intermittent screening data that leave the states of some nodes unresolved. Learning-based methods can introduce further information loss by compressing available network and state information into summary statistics. To retain the correspondence between node states and network positions, we develop Graph-Sequence Transformer Attention (GTA), which uses observed node states, network topology, and observation times to infer infection and recovery probabilities for susceptible-infectious-recovered spreading. We compare GTA with summary-based XGBoost and a one-dimensional convolutional neural network and with maximum-likelihood estimation of the recovery probability. Across four synthetic network classes and five empirical topologies, the three learning methods often perform comparably and respond similarly to changes in network size, mean degree, and observation timing. GTA is usually most accurate for estimating infection on sparse, heterogeneous networks, whereas summary-based methods often match or outperform it on denser, more homogeneous networks. For a fixed number of observations, wider spacing can initially improve inference by covering more of the spreading trajectory, but eventually increases error as intermediate transitions are missed. Maximum-likelihood estimation can outperform learning methods when recovery transitions are well resolved, but deteriorates as observations become more widely separated. Losing information about node states can compromise performance more than losing information about edges. Overall, the results show how inference from incomplete observations depends on network structure, temporal sampling, and the information retained in the observations.

We investigate field-induced director reorientation in nematic liquid crystals within the Frank-Oseen continuum framework through a global phase-space formulation that reveals the nonlinear geometric structure of equilibrium director configurations and their connection to the classical Fréedericksz transition. Reformulating the governing second-order equation as an autonomous dynamical system using a dimensionless spatial coordinate, we characterize the global organization of equilibrium states as a function of dimensionless control parameter |λ| = (L/ξH)2, which quantifies the competition between magnetic and elastic torques. The analysis reveals a supercritical pitchfork bifurcation of the bulk spatial dynamical system at λ = 0, marking the onset of symmetry breaking and generating an alternating sequence of stable centers and unstable saddles. The separatrix trajectories connecting neighboring saddles are identified as static topological solitons (domain walls), providing a natural geometric framework for characterizing their spatial width, energy, and stability. An associated three-dimensional energy-landscape representation provides a direct connection between phase-space topology and physical multistability, demonstrating how finite-cell boundary anchoring unfolds the idealized bulk bifurcation into the experimentally observed Fréedericksz transition. These results establish a unified geometric framework connecting nonlinear dynamical systems theory with continuum liquid-crystal physics, providing new physical insight into symmetry breaking, multistability, and localized topological structures in anisotropic soft matter.

We have developed a numerical method to identify invariant-circle families in island-around-island hierarchies and distinguish island regions (including sticky layers) from the surrounding chaotic sea in area-preserving maps. The method uses a rotation-angle representation constructed with delay coordinates, estimates rotation numbers with an evaluated error bound, determines resonance mode numbers of island chains, and classifies orbit types through sparse sampling of the waveform of the rotation angle. Validity tests were performed using the standard map, with benchmarks against widely used methods. We also present a practical application to the magnetic field in the toroidal plasma confinement device Heliotron J. We found that the method achieves accurate extraction of topological information, despite its limitations in certain cases.

We investigate the persistence and regularity of spectral submanifolds (SSMs) in high-dimensional parametric dynamical systems undergoing a Hopf bifurcation. By analyzing how resonances in the linearized spectrum near bifurcation points limit the existence and smoothness of SSMs, a phenomenon that has been mostly overlooked, we show that low-order Taylor coefficients of the SSM expansion and the associated reduced dynamics persist smoothly through the bifurcation. This analysis generalizes to any local bifurcation and provides a clear estimate of the parameter ranges over which a parametric SSM model can be justified, thus illustrating how globally the model can be extended despite the presence of resonances near criticality. We demonstrate these findings on multiple examples, including a data-driven SSM approach to the lid-driven cavity flow. For that problem, we construct a parametric SSM-reduced model that accurately captures the full transition to periodic dynamics and the critical Reynolds number. These results provide a mathematical foundation for robust data- and equation-driven model reduction of fluid flows across bifurcations, enabling an accurate prediction of nonlinear dynamics across critical parameter regimes.

Arctic atmospheric circulation and near-surface temperature are physically coupled, yet it remains unclear whether their spatial coherence changes in the same way across seasons. Using ERA5 reanalysis for 1940-2024, we directly compare winter (DJF) and summer (JJA) anomalies of 500 hPa geopotential height (Z500) and 2 m air temperature (T2M) over the Arctic. We combine threshold-independent correlation-decay analysis with fixed-density climate networks to quantify both the geographical extent of coherence and the spatial organization of the strongest relationships. The two fields exhibit opposite seasonal behavior. Z500 is more spatially coherent in winter, with its characteristic correlation length decreasing from approximately 1728 km in DJF to 1259 km in JJA. T2M shows the reverse pattern, with its correlation length increasing from approximately 1275 km in DJF to 1778 km in JJA. Climate-network analysis locates these changes geographically: winter Z500 connectivity is broadly distributed across the Arctic, whereas summer T2M connectivity strengthens and expands over the central Arctic Ocean. The seasonal transition, therefore, does not produce a uniform change in Arctic atmospheric organization. Instead, it is characterized by stronger basin-scale dynamical coherence in winter and enhanced near-surface thermodynamic coherence in summer. By comparing circulation and temperature within a common quantitative framework, this study demonstrates that physical coupling does not imply parallel seasonal organization and provides a baseline for assessing future changes in the spatial structure of Arctic atmospheric variability.