35 papers
This paper introduces a deformation-based framework for static billiards that utilizes the Jacobian determinant in noncanonical angular coordinates to reveal structured local phase-space expansion and contraction, demonstrating how these local variations globally balance to preserve area and correlate with invariant manifolds and periodic orbits.
This paper demonstrates through both numerical simulations and physical experiments that two coupled identical chaotic Lorenz oscillators exhibit simultaneous deterministic coherence and anti-coherence resonances in their respective state variables when the coupling strength is below the threshold for complete synchronization, a regime characterized by hyperchaotic dynamics and on-off intermittency.
This paper presents a compact dynamical mean-field theory for large networks of coupled phase oscillators that preserves $2\pi$-periodicity and disorder averaging to derive a self-consistent single-oscillator stochastic equation, successfully bridging microscopic phase response data with macroscopic synchronization predictions for arbitrary phase-reducible systems.
This paper demonstrates that while the self-similar photon ring structure of a Kerr black hole persists in phase space without exhibiting chaos, deforming the spacetime away from the Kerr geometry induces chaotic dynamics near resonant bound orbits, resulting in a fractal phase-space structure encoded in the first-return map.
This paper reveals a layered organization in the Kuramoto-Sivashinsky equation's state space where multiple invariant sets, including chaotic attractors and periodic orbits, coexist and are selected by initial energy levels, a phenomenon linked to continuous spatial translational symmetry.
This paper utilizes numerical simulations of chaotic intermittency dynamics in a finite 3D Z(3) spin lattice to reveal a complex phase behavior characterized by a second-order transition with hysteresis and resonances, a hybrid universality class combining mean-field and 3D Ising features, and a weak first-order transition via a tricritical crossover.
This paper proposes a deep learning framework that jointly discovers optimal coordinates and flow maps to enable precise, computationally efficient time-stepping for multiscale systems, achieving state-of-the-art predictive accuracy with reduced costs on complex models like the Fitzhugh-Nagumo neuron and Kuramoto-Sivashinsky equations.
Using high-resolution simulations, this study reveals that kinetic energy dissipation in subsonic turbulence is vorticity-dominated, localized on small scales, and lags energy injection by approximately 1.64 turnover times, whereas supersonic dissipation is density-correlated, spans multiple scales via shocks and vorticity, and lags by only 0.48 turnover times, with distinct fractal structures identified in both regimes.
This paper introduces a geometric framework of Covariant Multi-Scale Negative Coupling on dynamic Riemannian manifolds to counteract dimensional reduction in dissipative PDEs, theoretically proving the finite dimensionality of global attractors while numerically validating the mechanism's ability to stabilize high-dimensional structural complexity against macroscopic dissipation.
This paper identifies a novel mechanism called "pseudo-coherence," where non-normal pseudospectral amplification in linearly stable, non-oscillatory stochastic systems drives a sharp transition to intermittent collective temporal organization and irreversible currents without requiring intrinsic oscillators or dynamical instabilities.
This paper argues that the late emergence of chaos theory in the 1960s, despite its mathematical foundations being established by Poincaré and his colleagues decades earlier, was primarily caused by the strict empiricist tenets of positivism, which led to the dismissal of chaotic systems as "useless" and "meaningless" mathematics due to their perceived lack of grounding in experience.
This paper establishes a low-dimensional dynamical framework for two-dimensional vertical falling films to identify and characterize exact coherent states—such as travelling waves, relative periodic orbits, and equilibria—that underpin the system's chaotic interfacial dynamics.
This paper demonstrates that utilizing unconventionally large learning rates to induce transient chaotic dynamics during neural network training creates an optimal balance between exploration and exploitation, thereby accelerating convergence to high accuracy across various architectures and tasks.
This paper introduces Smooth Prototype Equivalences (SPE), a framework utilizing invertible neural networks to match sparse, noisy empirical observations to prototypical dynamical behaviors, enabling the equation-free identification of invariant structures and classification of dynamical regimes in complex biological and physical systems.
This paper introduces two interpretable symbolic machine learning methods, the Symbolic Neural Forecaster (SyNF) and the Symbolic Tree Forecaster (SyTF), which successfully learn explicit algebraic equations to forecast chaotic time series with accuracy competitive to deep learning while providing transparent insights into the underlying dynamics.
This paper demonstrates that deterministic chaos can emerge in bounded 3D dynamical systems even when the Jacobian is pointwise spectrally contracting, revealing that non-normality-driven transient amplification via endogenous switching constitutes a distinct route to chaos independent of spectral criticality.
The paper introduces Panda, a pretrained foundation model for chaotic dynamics that, despite being trained exclusively on synthetic low-dimensional ordinary differential equations, demonstrates emergent zero-shot forecasting capabilities for unseen chaotic systems, real-world experimental data, and even partial differential equations.
This paper combines non-linear shock wave theory with frame-by-frame video analysis of the 2020 Beirut explosion to derive the Landau-Whitham formula for overpressure layer thickness and demonstrate strong agreement between theoretical predictions and observational data.
This paper proposes a fully data-driven framework that combines adaptively computed, mechanism-aware precursors based on Optimal Time-Dependent (OTD) modes with a Transformer model to significantly extend the prediction horizons for extreme events in high-dimensional chaotic systems like Kolmogorov flow without requiring knowledge of the underlying governing equations.
This paper presents a framework for identifying and analyzing dynamics-induced active-inactive cluster patterns in complex networks that arise from symmetry breaking in systems with odd intrinsic dynamics and coupling, demonstrating that such patterns can exist without requiring network symmetries and providing a stability analysis based on coupling strength and intercluster weights.