Dynamical Systems

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Overview

Dynamical systems describe how a system's state changes over time and explain behaviors such as equilibria, oscillations, attractors, bifurcations, and chaos. Researchers analyze these behaviors mathematically and learn models from data using approaches such as Koopman operators, neural ODEs, physics-informed networks, and structure-preserving Hamiltonian models. Applications range from forecasting Lorenz and pendulum dynamics to modeling reaction-diffusion processes, neural activity, and robot motion, often with control and safety guarantees. A central challenge is that accurate short-term predictions do not ensure faithful long-term behavior: learned models can drift, violate physical constraints, or fail to generalize to unseen regimes.

Latest papers

CardsList

482 papers56 papers in the last four weeks, up 19% on the four weeks before. 0.3% of all new papers.

  1. Design and Aerodynamic Modeling of MetaMorpher: A Hybrid Rotary andFixed-Wing Morphing UAV

    Mar 31, 2026Anja Bosak, Dorian Erić, Ana Milas +1Aerial RoboticsDynamical Systems

    All authors are with the University of Zagreb, Faculty of Electrical Engineering and Computing, LARICS Laboratory for Robotics and Intelligent Control Systems, Unska 3, 10000 Zagreb, Croatia

  2. Predictor-Based Output-Feedback Control of Linear Systems with Time-Varying Input and Measurement Delays via Neural-Approximated Prediction Horizons

    Mar 31, 2026Luke Bhan, Miroslav Krstic, Yuanyuan ShiFeedback ControlDynamical Systems

    Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093-0411, USA · Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0411, USA

  3. Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks

    Mar 28, 2026Shafayeth Jamil, Rehan KapadiaStructure-Preserving Neural NetworksDynamical Systems

    Department of Electrical and Computer Engineering, University of Southern California

  4. Comparing Physics-Informed and Neural ODE Approaches for Modeling Nonlinear Biological Systems: A Case Study Based on the Morris-Lecar Model

    Mar 27, 2026Nikolaos M. Matzakos, Chrisovalantis SfyrakisPhysics-Informed MLNeural ODEs

    Department of Education, School of Pedagogical and Technological Education (ASPETE), 141 21 Athens, Greece. · Department of Mechanical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), 151 22 Athens, Greece.

  5. Conchordal: Emergent Harmony via Direct Cognitive Coupling in a Psychoacoustic Landscape

    Mar 26, 2026Koichi TakahashiMusic GenerationEmergent Behavior in Multi-Agent Systems

    Institute for Advanced Biosciences and Graduate School of Media and Governance, Keio University

  6. Dynamical Systems Theory Behind a Hierarchical Reasoning Model

    Mar 24, 2026Vasiliy A. Es'kin, Mikhail E. SmorkalovSudoku SolvingNeural Algorithmic Reasoning

    Department of Radiophysics, University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia · Huawei Nizhny Novgorod Research Center, Nizhny Novgorod 603006, Russia · Skolkovo Institute of Science and Technology, Moscow 121205, Russia

  7. Generalizing Dynamics Modeling More Easily from Representation Perspective

    Mar 24, 2026Yiming Wang, Zhengnan Zhang, Genghe Zhang +7Dynamical SystemsLatent Dynamics Modeling

    College of Computer Science and Technology, and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, China · College of Software and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, China · School of Computing, Belfast, Northern Ireland, UK +1

  8. Identifiability and amortized inference limitations in Kuramoto models

    Mar 23, 2026Emma Hannula, Jana de Wiljes, Matthew T. Moores +2Kuramoto ModelAmortized Inference

    LUT University, Yliopistonkatu 34, Lappeenranta, 53850, Finland · TU Ilmenau, Ehrenbergstraße 29, Ilmenau, 98693, Germany · University of Cambridge, Herschel Road, Cambridge, CB3 9AL, United Kingdom

  9. Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach

    Mar 23, 2026Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1Dynamical SystemsNeural PDE Solvers

    Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, 21218, MD, USA · Dept. of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, 21218, MD, USA · School of Chemical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Street, Athens, 15772, Greece +2

  10. FluidWorld: Reaction-Diffusion Dynamics as a Predictive Substrate for World Models

    Mar 22, 2026Fabien PollyReaction-Diffusion SystemsWorld Model Learning

    Independent Researcher

  11. LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models

    Mar 21, 2026Amirmohammad Ziaei Bideh, Jonathan GryakODE DiscoveryDynamical Systems

    The Graduate Center, CUNY New York, New York, USA · Queens College and The Graduate Center, CUNY New York, New York, USA

  12. From Data to Laws: Neural Discovery of Conservation Laws Without False Positives

    Mar 20, 2026Rahul D RayScientific DiscoveryDynamical Systems

    Department of Electronics and Electrical Engineering, BITS Pilani, Hyderabad Campus

  13. Formulation and Learning Of The Forecasting Problem

    Mar 20, 2026Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki +2Data AssimilationOperator Learning

    California Institute of Technology, Pasadena, CA · Oregon State University, Corvallis, OR · NVIDIA Corporation, Santa Clara, CA +1

  14. Structural Controllability of Large-Scale Hypergraphs

    Mar 20, 2026Joshua Pickard, Xin Mao, Can ChenDynamical Systems

    Eric and Wendy Schmidt Center, Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA · School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA · Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA +1

  15. K-GMRF: Kinetic Gauss-Markov Random Field for First-Principles Covariance Tracking on Lie Groups

    Mar 20, 2026ZhiMing LiCovariance EstimationVisual Object Tracking

    School of Computer Science and Technology, Tianjin University

  16. Extending SSMs with the Exponentially Weighted Signature

    Mar 19, 2026Alexandre Bloch, Benjamin Walker, Joël Mouterde +3Dynamical SystemsTime Series Classification

    Mathematical Institute, University of Oxford · SKF · Department of Mathematics, Imperial College London

  17. Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC

    Mar 19, 2026Julian Martinez, Kooktae LeeInput-to-State StabilityMulti-Agent Control

    Department of Mechanical and Aerospace Engineering, Texas Tech University, Lubbock, TX 79409, USA

  18. Towards Infinitely Long Neural Simulations: Self-Refining Neural Surrogate Models for Dynamical Systems

    Mar 18, 2026Qi Liu, Laure Zanna, Joan BrunaNeural Surrogate ModelingAutoregressive Modeling

    Courant Institute School of Mathematics, Computing, and Data Science, New York University, USA.

  19. Data-driven model order reduction for structures with piecewise linear nonlinearity using dynamic mode decomposition

    Mar 18, 2026Akira Saito, Masato TanakaReduced-Order ModelingDynamical Systems

    Department of Mechanical Engineering, Meiji University, Kawasaki, Kanagawa 214-8571, Japan. · Toyota Research Institute of North America Toyota Motor North America, Inc. Ann Arbor, Michigan, 48105, USA

  20. Mathematical Modeling of Cancer-Bacterial Therapy: Analysis and Numerical Simulation via Physics-Informed Neural Networks

    Mar 18, 2026Ayoub Farkane, David LassounonReaction-Diffusion SystemsOncology

    TICLab, International University of Rabat, Rabat, 11100, Morocco · Université de Lorraine, CNRS, CRAN, F-54000 Nancy, France · Université de Lorraine, CNRS, IECL, F-54000, Nancy, France +1

  21. Unifying Optimization and Dynamics to Parallelize Sequential Computation: A Guide to Parallel Newton Methods for Breaking Sequential Bottlenecks

    Mar 17, 2026Xavier GonzalezLyapunov Exponent EstimationDynamical Systems

    STANFORD UNIVERSITY

  22. Data-driven forced response analysis with min-max representations of nonlinear restoring forces

    Mar 17, 2026Akira Saito, Hiromu FujitaNonlinear System IdentificationDynamical Systems

    Department of Mechanical Engineering, Meiji University, Kawasaki, Kanagawa 214-8571, Japan.

  23. Trajectory-Optimized Time Reparameterization for Learning-Compatible Reduced-Order Modeling of Stiff Dynamical Systems

    Mar 17, 2026Joe Standridge, Daniel Livescu, Paul CizmasReduced-Order ModelingDynamical Systems

    Texas A&M University, College Station, Texas 77840 · Los Alamos National Laboratory, Los Alamos, New Mexico 87545

  24. Early-Terminable Energy-Safe Iterative Coupling for Parallel Simulation of Partitioned Port-Hamiltonian Systems

    Mar 17, 2026Qi Wei, Jianfeng Tao, Hongyu Nie +1Dynamical SystemsPort-Hamiltonian Systems

    School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

  25. A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients

    Mar 16, 2026Seungwan Han, Kwanghyuk Park, Jiaxi Gu +1Reaction-Diffusion SystemsPDE Solving

  26. Storage and selection of multiple chaotic attractors in minimal reservoir computers

    Mar 16, 2026Francesco Martinuzzi, Holger KantzReservoir ComputingDynamical Systems

    Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

  27. Ultra-Early Prediction of Tipping Points: Integrating Dynamical Measures with Reservoir Computing

    Mar 16, 2026Xin Li, Qunxi Zhu, Chengli Zhao +4Early Warning DetectionDynamical Systems

    College of Science, National University of Defense Technology, Changsha, Hunan 410073, China · Research Institute of Intelligent Complex Systems and MOE Frontiers Center for Brain Science, Fudan University, Shanghai 200433, China · School of Mathematical Sciences, SCMS, SCAM, and CCSB, Fudan University, Shanghai 200433, China +1

  28. Physically Accurate Rigid-Body Dynamics in Particle-Based Simulation

    Mar 15, 2026Ava Abderezaei, Nataliya Nechyporenko, Joseph Miceli +2Physics-Based SimulationRobotics Simulation

    Department of Computer Science, University of Colorado Boulder, CO, USA

  29. Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems

    Mar 13, 2026Hongchao Zhang, Mohamad H. Kazma, Meiyi Ma +2Control Barrier FunctionsDynamical Systems

    Department of Computer Science, Vanderbilt University, Nashville, TN 37235 USA. · Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235 USA.

  30. Clustering Astronomical Orbital Synthetic Data Using Advanced Feature Extraction and Dimensionality Reduction Techniques

    Mar 13, 2026Eraldo Pereira Marinho, Nelson Callegari Junior, Fabricio Aparecido Breve +1Dynamical Systems

    Institute of Geosciences and Exact Sciences (IGCE), Unesp, Rio Claro, Brazil.