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

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

  1. Emergence Transformer: Dynamical Temporal Attention Matters

    Apr 18, 2026Zihan Zhou, Bo-Wei Qin, Kai Du +1Dynamical SystemsTemporal Attention

    School of Mathematical Sciences and Shanghai Center for Mathematical Sciences, Fudan University, 200433 Shanghai, China · Research Institute of Intelligent Complex Systems, Fudan University, 200433 Shanghai, China · Shanghai Artificial Intelligence Laboratory, 200232 Shanghai, China +1

  2. Spectral Kernel Dynamics for Planetary Surface Graphs: Distinction Dynamics and Topological Conservation

    Apr 17, 2026Jnaneshwar DasDynamical SystemsSpectral Methods

    School of Earth and Space Exploration, Arizona State University

  3. Stability and Generalization in Looped Transformers

    Apr 16, 2026Asher LabovichNeural Network GeneralizationDynamical Systems

  4. A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning

    Apr 16, 2026Anand Gokhale, Anton V. Proskurnikov, Yu Kawano +1Dynamical SystemsContraction Theory

    Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA 93106 USA · Department of Electronics and Telecommunications, Politecnico di Torino, Italy, 10129 · Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

  5. One-shot learning for the complex dynamical behaviors of weakly nonlinear forced oscillators

    Apr 16, 2026Teng Ma, Luca Rosafalco, Wei Cui +2Dynamical SystemsSparse Identification of Nonlinear Dynamics

  6. On Common Misconceptions in Classical Vehicle Dynamics

    Apr 14, 2026Massimo GuiggianiVehicle DynamicsDynamical Systems

    Department of Civil and Industrial Engineering, Universit`a di Pisa, Italy

  7. Stability and Geometry of Attractors in Neural Cellular Automata

    Apr 14, 2026Mia-Katrin Kvalsund, James StovoldNeural Cellular AutomataNeural Network Robustness

    Department of Physics, University of Oslo, Norway · Department of Computer Science, University of York, UK

  8. Asymptotically Stable Gait Generation and Instantaneous Walkability Determination for Planar Almost Linear Biped with Knees

    Apr 14, 2026Fumihiko Asano, Ning Lei, Taiki SedoguchiRobot LocomotionHumanoid Robot Locomotion

    Graduate School of Advanced Science and Technology, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

  9. Dynamic Modeling and Robust Gait Optimization of a Compliant Worm Robot

    Apr 13, 2026Xinyu Zhou, Yu Mei, Faith Thomson +3Robot LocomotionEnergy-Efficient Robot Locomotion

    Michigan State University, East Lansing, MI 48824 USA

  10. Multi-Head Residual-Gated DeepONet for Coherent Nonlinear Wave Dynamics

    Apr 13, 2026Zhiwei Fan, Yiming Pan, Daniel CocaDeep Operator NetworksNeural Operators

    School of Engineering, Newcastle University, NE1 7RU, United Kingdom · School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China

  11. Learning to Test: Latent Representation Learning for Dynamic Instability Detection

    Apr 13, 2026Minxing Zheng, Zewei Deng, Liyan Xie +1Dynamical SystemsPhysics-Informed ML

    Carnegie Mellon University · University of Minnesota

  12. Visualising the Attractor Landscape of Neural Cellular Automata

    Apr 12, 2026James Stovold, Mia-Katrin Kvalsund, Harald Michael Ludwig +2Neural Cellular AutomataNeural Network Interpretability

    University of York, UK · University of Oslo, Norway · Machine Learning Research Unit, TU Wien, Austria +2

  13. Safety Guarantees in Zero-Shot Reinforcement Learning for Cascade Dynamical Systems

    Apr 12, 2026Shima Rabiei, Sandipan Mishra, Santiago PaternainZero-Shot RLSafe RL

    The authors are with the Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute. · The author is with the Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute.

  14. On Feedback Speed Control for a Planar Tracking

    Apr 10, 2026Xincheng Li, Tengyue Liu, Udit HalderInput-to-State StabilityMulti-Robot Formation Control

    Department of Mechanical and Aerospace Engineering, University of South Florida

  15. Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations

    Apr 9, 2026Finn Sommer, Vamika Rathi, Sebastian Goetschel +1Dynamical SystemsComputational Fluid Dynamics

    Chair Computational Mathematics, Institute of Mathematics, Hamburg University of Technology, 21073 Hamburg, Germany

  16. Robust Learning of Heterogeneous Dynamic Systems

    Apr 7, 2026Shuoxun Xu, Zijian Guo, Brooke R. Staveland +2Dynamical SystemsRobust Estimation

    University of California at Berkeley · Zhejiang University · University of California at San Francisco

  17. Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots

    Apr 6, 2026Varun Madabushi, Akash Harapanahalli, Samuel Coogan +1Dynamical SystemsReachability Analysis

    School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA.

  18. Finite-Step Invariant Sets for Hybrid Systems with Probabilistic Guarantees

    Apr 6, 2026Varun Madabushi, Elizabeth Dietrich, Hanna Krasowski +1Dynamical Systems

    Georgia Institute of Technology · University of California, Berkeley

  19. Lotka-Sharpe Neural Operators for Control of Population PDEs

    Apr 4, 2026Miroslav Krstic, Iasson Karafyllis, Luke Bhan +1Feedback ControlPDE Operator Learning

    University of California, San Diego, USA · National Technical University of Athens, Greece · KTH Royal Institute Technology, Stockholm, Sweden

  20. On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations

    Apr 3, 2026Santosh Mohan Rajkumar, Dibyasri Barman, Kumar Vikram Singh +1Extended Dynamic Mode DecompositionDynamical Systems

    Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA. · Department of Chemical, Paper, and Biomedical Engineering at Miami University, Oxford, OH, USA. · Department of Mechanical and Manufacturing Engineering at Miami University, Oxford, OH, USA.

  21. A Dynamic Toolkit for Transmission Characteristics of Precision Reducers with Explicit Contact Geometry

    Apr 2, 2026Jiacheng Miao, Chao Liu, Qiliang Wang +2Dynamical SystemsMultibody Dynamics

    Intelligent Equipment Division, CRRC Qishuyan Institute Co., Ltd, Changzhou, 213011, China · School of Mechanical Engineering, Dalian Jiaotong University, Dalian, 116028, China · Research Institute, CRRC Qishuyan Institute Co., Ltd, Changzhou, 213011, China

  22. Oscillator-Based Associative Memory with Exponential Capacity: Theory, Algorithms, and Hardware Implementation

    Apr 1, 2026Arie Ogranovich, Taosha Guo, Arvind R. Venkatakrishnan +3Kuramoto ModelAssociative Memory

    Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, 93106, USA · Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA, 92697, USA

  23. Bias Inheritance in Neural-Symbolic Discovery of Constitutive Closures Under Function-Class Mismatch

    Apr 1, 2026Hanbing Liang, Ze Tao, Fujun LiuReaction-Diffusion SystemsPDE Discovery

    Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology, Changchun 130022, P.R. China

  24. Integer-State Dynamics of Quantized Spiking Neural Networks for Efficient Hardware Acceleration

    Apr 1, 2026Lei ZhangSpiking Neural NetworksNeuromorphic Computing

    Faculty of Engineering and Applied Science, University of Regina

  25. Predicting Dynamics of Ultra-Large Complex Systems by Inferring Governing Equations

    Apr 1, 2026Qi Shao, Duxin Chen, Jiawen Chen +5Dynamical SystemsNonlinear System Identification

    School of Mathematics, Southeast University, Nanjing, 210096, P. R. China. · School of Electronic Engineering and Computer Science, Queen Mary University of London, London, E1 4NS, UK. · School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK. +4

  26. Activation Saturation and Floquet Spectrum Collapse in Neural ODEs

    Apr 1, 2026Nikolaos M. MatzakosLyapunov Exponent EstimationNeural ODEs

    Currently visiting the Department of Mathematics, Chair of Dynamics, Control, Machine Learning and Numerics, Friedrich-Alexander-Universität Erlangen–Nürnberg (FAU), 91058 Erlangen, Germany.

  27. Hierarchical Motion Planning and Control under Unknown Nonlinear Dynamics via Predicted Reachability

    Mar 31, 2026Zhiquan Zhang, Melkior OrnikMotion PlanningDynamical Systems

    University of Illinois Urbana-Champaign, IL, 61801 USA.

  28. Set-Based Value Function Characterization and Neural Approximation of Stabilization Domains for Input-Constrained Discrete-Time Systems

    Mar 31, 2026Mohamed Serry, S. Sivaranjani, Jun LiuDynamical SystemsValue Function Estimation

    Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada. · Department of Mechanical and Mechatronics Engineering at the University of Waterloo. · School of Industrial Engineering, Purdue University, 15 N Grant Street, West Lafayette, 47907, Indiana.

  29. Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

    Mar 31, 2026Simone Betteti, Luca LaurentiEnergy-Based ModelsDynamical Systems

    RIAS Lab, The Italian Institute of Artificial Intelligence for Industry, Turin, 10129, IT · Delft Center for Systems and Control, TU Delft, Delft, 2600 AA, The Netherlands

  30. HyperKKL: Learning KKL Observers for Non-Autonomous Nonlinear Systems via Hypernetwork-Based Input Conditioning

    Mar 31, 2026Yahia Salaheldin Shaaban, Abdelrahman Sayed Sayed, M. Umar B. Niazi +1Dynamical Systems

    Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, UAE. · Univ Gustave Eiffel, COSYS-ESTAS, F-59657 Villeneuve d’Ascq, France. · Department of Decision and Control Systems and Digital Futures, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden.