Nonlinear Dynamics
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Related Articles from SNS
AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression
Announce Type: new Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency. However, nonlinear dynamics are so complex that capturing dynamically changing nonlinear patterns and utilizing them for downstream tasks under strict time constraints is nontrivial. To bridge the gap between nonlinear complexity and computational tractability, this study applies Koopman...
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
arXiv:2412.12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of data-driven discovery in nonlinear dynamical systems, these methods have garnered significant attention. Among them, Sparse Identification of Nonlinear Dynamics (SINDy) has emerged as a transformative approach,...
Certified Neural Approximations of Nonlinear Dynamics
arXiv:2505.15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system. To address this fundamental challenge, we propose a novel, adaptive, and parallelizable verification method based...
Bayesian Inference of Nonlinear Malaria Dynamics in Ghana via an Ensemble Markov Chain Monte Carlo Sampler
arXiv:2606.00783v1 Announce Type: cross Abstract: Reliable quantification of malaria dynamics in sub-Saharan Africa is hindered by short, noisy, and spatially heterogeneous surveillance records. In Ghana, health-facility data from 2014 to 2023 reveal non-linear and age-specific fluctuations in hospital admissions, yet existing approaches struggle to capture stochastic variability or provide credible uncertainty bounds. This study develops a Bayesian nonlinear inference framework that...
Predicting and controlling nonlinear neuro-mechanical locomotion dynamics
arXiv:2605.03362v1 Announce Type: cross Abstract: Neuromechanics aims to understand the link between an animal's neural activity and its physical behaviors. Recent advances in experimental and machine learning techniques enable simultaneous recordings of neural and locomotion dynamics over long time periods and across multiple behavioral transitions in worms, flies, and other organisms. These high-dimensional datasets present the challenge of inferring interpretable low-dimensional dynamical...
Quantum algorithms for stochastic nonlinear differential equations
arXiv:2606.08349v1 Announce Type: cross Abstract: Stochastic nonlinear dynamics underlie many models in engineering and computational physics, yet accurate high-dimensional simulation remains challenging. We present a quantum algorithm for a broad class of $N$-dimensional stochastic differential equations with dissipation and quadratic drift. The algorithm applies to strongly nonlinear systems with all-to-all interactions, thereby extending the scope of previously known quantum algorithms...
Breakdown of Adiabatic Scaling and Noise-Induced Functional Synchronization in Deeply Quiescent Excitable Systems
arXiv:2605.06692v3 Announce Type: replace-cross Abstract: Coherence resonance (CR) 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 (SRK) model driven by multiplicative Feller noise. We show that traditional extremal evaluations of CR encounter a "bathtub effect", a...
Competitive Instability in Judo: The Hidden Mechanism within an AI-Driven Non-Linear Dynamics Framework
Announce Type: new Abstract: This study presents a unified nonlinear dynamical framework for understanding, modelling, and teaching competitive judo. The Tori Uke dyad is formalised as a constrained multi body system whose behaviour emerges from symmetry breaking,coupling dynamics and transitions between attractor basins. Two fundamental instability archetypes rotational collapse Uchi mata type and gravitational lever collapse Seoi otoshi,suwari version, are identified as the core pathways...
A model-free approach to control barrier functions for higher-order systems
arXiv:2606.04790v1 Announce Type: new Abstract: Control barrier functions (CBFs) are a widely applied modular tool to ensure safe operation of nonlinear dynamical control systems. However, for their construction accurate knowledge of the system dynamics is typically needed. This requirement was recently alleviated for relative-degree-one systems using techniques from prescribed performance control (PPC) or funnel control (FC).
Towards Guaranteed Optimal PID Tuning for Uncertain Nonlinear Systems
arXiv:2606.04787v1 Announce Type: new Abstract: Despite the widespread use of PID controllers in engineering practice, designing optimal PID parameters has long been regarded as a challenging problem in both theory and practice, particularly when faced with uncertain nonlinear dynamical systems. Based on the authors' PID control theory established recently for MIMO nonlinear uncertain systems (Zhao and Guo, 2022), which provides a concrete PID parameter set for global stability of PID...