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. Active-learning mapping of the Vicsek model phase diagram

    Apr 30, 2026Grace T. Bai, Brandon B. LeDynamical SystemsPhase Transitions

    Department of Computer Science, University of Virginia, Charlottesville, Virginia 22904, USA · Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA

  2. Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models

    Apr 29, 2026Andrea Agazzi, Giuseppe Bruno, Eloy Mosig García +2Dynamical SystemsTransformer

    Department of Mathematics and Statistics, University of Bern (CH) · Department of Mathematics, University of Pisa (IT)

  3. A Dynamical Framework for Cognitive Processes Based on Transformations and Semantic Equivalence

    Apr 29, 2026Carlo Cattani, Dioneia Motta Monte-SerratDynamical SystemsCognitive Modeling

    Engineering School, DEIM, University of Tuscia, (VT), 01100, Italy · Department of Physics, University of Sao Paulo, USP; Department of Law, University of Ribeirao Preto, Unaerp, Brazil.

  4. Population Dynamics in ARIEL Robotics Systems Featuring Embodied Evolution via Spatial Mating Mechanisms

    Apr 29, 2026Victoria Peterson, Akshat Srivastava, Raghav PrabhakarDynamical SystemsEvolutionary Optimization

    Vrije Universiteit Amsterdam, Netherlands

  5. Inferring bifurcation diagrams of two distinct chaotic systems by a single machine

    Apr 29, 2026Jianmin Guo, Yao Du, Yizhen Yu +2Dynamical SystemsNonlinear System Identification

    School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China · College of Physics and Electronic Information Engineering, Qinghai Normal University, Xining 810008, China · School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China

  6. Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control

    Apr 28, 2026Ankur Kamboj, Biswadip Dey, Vaibhav SrivastavaDynamical SystemsFeedback Control

    Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824 · Meta Reality Labs, Redmond, WA 98052

  7. Teacher Forcing as Generalized Bayes: Optimization Geometry Mismatch in Switching Surrogates for Chaotic Dynamics

    Apr 28, 2026Andre Herz, Daniel Durstewitz, Georgia KoppeNeural Surrogate ModelingGeneralized Bayesian Inference

    Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany · Dept. of Theoretical Neuroscience, Central Institute of Mental Health (CIMH), Mannheim, Germany · Hector Institute for AI in Psychiatry and Dept. of Psychiatry and Psychotherapy, CIMH, Mannheim, Germany +1

  8. Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching

    Apr 28, 2026Yuhe Bai, Chengli Tan, Jiaqi Li +2Dynamical SystemsRegime-Switching Dynamical Systems

    School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China · School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, China

  9. Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics

    Apr 28, 2026Arnau Vivet, Alex ArenasSoftmax AttentionDynamical Systems

    1Departament d’Enginyeria Inform`atica i Matem`atiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain · 2Complexity Science Hub Vienna, Metternichgasse 8, 1030 Vienna, Austria

  10. Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data

    Apr 27, 2026K. Michael Martini, Eslam Abdelaleem, Paarth Gulati +1Dynamical SystemsInformation Bottleneck

    Department of Physics, Emory University, Atlanta, GA, USA · Schools of Physics and Psychology, Georgia Institute of Technology, Atlanta, GA, USA · Initiative in Theory and Modeling of Living Systems, Emory University, Atlanta, GA, USA +1

  11. Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs

    Apr 27, 2026Olivier BournezDynamical SystemsReLU Neural Networks

    Institut Polytechnique de Paris, Ecole Polytechnique, LIX, Palaiseau, France

  12. Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions

    Apr 27, 2026Qinhan Hou, Jing TangDynamical SystemsGraph Structure Learning

    Doctoral Program of Computer Science, University of Helsinki, Helsinki, Finland · Research Program in Systems Oncology, Faculty of Medicine, University of Helsinki, Helsinki, Finland

  13. Cardiac Stability Theory: An Axiomatically Grounded Framework for Continuous Cardiac Health Monitoring via Smartphone Photoplethysmography

    Apr 26, 2026Timothy Oladunni, Farouk Ganiyu AdewumiDynamical SystemsPhotoplethysmography

    Department of Computer Science, Morgan State University, Baltimore, MD 21251, USA

  14. Hamiltonian Graph Inference Networks: Joint structure discovery and dynamics prediction for lattice Hamiltonian systems from trajectory data

    Apr 26, 2026Ru Geng, Panayotis Kevrekidis, Yixian Gao +2Dynamical SystemsGraph Structure Learning

    School of Mathematics and Statistics, Changchun University, Changchun, 130022, China · Department of Mathematics and Statistics, University of Massachusetts, Amherst, 01003, MA, USA · Department of Physics, University of Massachusetts, Amherst, 01003, MA, USA +2

  15. Learning Control Policies to Provably Satisfy Hard Affine Constraints for Black-Box Hybrid Dynamical Systems

    Apr 24, 2026Aayushi Shrivastava, Kartik Nagpal, Sairam Jinkala +2Dynamical SystemsSafety-Critical Control

    Department of Mechanical Engineering, University of California Berkeley, Berkeley, CA 94709, USA

  16. Model Predictive Control of Hybrid Dynamical Systems

    Apr 23, 2026Ricardo G. Sanfelice, Berk AltinDynamical SystemsModel Predictive Control

    Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA, 94107 USA

  17. Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs

    Apr 23, 2026Mahadev Sunil Kumar, Adarsh GanesanDynamical SystemsReservoir Computing

    Amrita School of Computing, Amrita Vishwa Vidyapeetham, Kollam, India 690525 · Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani – Dubai Campus, Dubai, United Arab Emirates 345055

  18. On the algebra of Koopman eigenfunctions and on some of their infinities

    Apr 23, 2026Zahra Monfared, Saksham Malhotra, Sekiya Hajime +2Dynamical SystemsKoopman Operator Learning

    Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany. · Department of Mathematics and Computer Science, University of Heidelberg, Germany. · School of Computation, Information and Technology, Technical University of Munich, Germany & MDSI & MCML. +1

  19. A Case Study in Recovery of Drones using Discrete-Event Systems

    Apr 23, 2026Liam P. Burns, Dayse M. Cavalcanti, Felipe G. Cabral +4Dynamical SystemsAerial Robotics

    Department of Electrical and Computer Engineering and Ingenuity Labs Research Institute, Queen’s University, Kingston, ON, K7L 3N6, Canada · Automation and Systems Engineering Program, Federal University of Santa Catarina, Florianópolis, SC, 88.040-900, Brazil

  20. CLT-Optimal Parameter Error Bounds for Linear System Identification

    Apr 23, 2026Yichen Zhou, Stephen TuDynamical SystemsParameter Estimation

    Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California, USA.

  21. Learning Hippo: Multi-attractor Dynamics and Stability Effects in a Biologically Detailed CA3 Extension of Hopfield Networks

    Apr 22, 2026Daniele Corradetti, Renato CorradettiDynamical SystemsNeural Processes

    Grupo de Física Matemática Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisboa, Portugal · Dipartimento di Neuroscienze, Psicologia, Area del Farmaco e Salute del Bambino (NEUROFARBA) Università di Firenze, Italy22

  22. An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling

    Apr 22, 2026Anif N. Shikder, Ramit Dey, Sayantan Auddy +6Dynamical SystemsNeural Network Interpretability

    Department of Mathematics, Western University, London ON, Canada · Fields Lab for Network Computation, Fields Institute, Toronto ON, Canada · King’s University College at Western University, London ON, Canada +1

  23. A neural operator framework for data-driven discovery of stability and receptivity in physical systems

    Apr 21, 2026Chengyun Wang, Liwei Chen, Nils ThuereyDynamical Systems

    School of Computation, Information and Technology, Technical University of Munich, Boltzmannstrasse 3, D-85748 Garching bei München, Germany · Beijing Institute of Astronautical Systems Engineering, Beijing, China

  24. Forward Dynamics of Variable Topology Mechanisms - The Case of Constraint Activation

    Apr 21, 2026Andreas MuellerDynamical SystemsMultibody Dynamics

    Institute of Robotics, Johannes Kepler University Altenbergerstr. 69, 4040 Linz, Austria

  25. HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction

    Apr 20, 2026Blake Werner, Sergio A. Esteban, Massimiliano De Sa +2Dynamical SystemsHumanoid Robot Locomotion

    Caltech, Pasadena, CA, USA · NC State University, Raleigh, NC, USA

  26. Benchmarking System Dynamics AI Assistants: Cloud Versus Local LLMs on CLD Extraction and Discussion

    Apr 20, 2026Terry LeitchLLM QuantizationDynamical Systems

    Ruxton AI

  27. Physics-Informed Neural Networks for Biological 2D+t2\mathrm{D}{+}t Reaction-Diffusion Systems

    Apr 20, 2026William Lavery, Jodie A. Cochrane, Christian Olesen +3Dynamical SystemsReaction-Diffusion Systems

    Dept. of Information Technology Uppsala University Uppsala, Sweden · Dept. of Medical Genetics Oslo University Hospital Oslo, Norway · Dept. of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, USA +1

  28. Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systems

    Apr 20, 2026Youyuan Long, Gokhan Solak, Arash AjoudaniDynamical SystemsResidual Learning

    Human-Robot Interfaces and Interaction Lab, Istituto Italiano di Tecnologia, 16163 Genoa, Italy

  29. Locally invariant manifolds and foliations

    Apr 20, 2026Lachlan Ewen MacDonaldDynamical SystemsGradient Descent

  30. Locomotion of an Elastic Snake Robot via Natural Dynamics

    Apr 20, 2026Tristan Ehlert, Arne Sachtler, Annika Schmidt +2Dynamical SystemsEnergy-Efficient Robot Locomotion

    German Aerospace Center (DLR), Robotics and Mechatronics Center (RMC), Münchner Str. 20, 82234 Weßling, Germany · Technical University of Munich (TUM), Department of Computer Engineering; Boltzmannstraße 3, 85748 Garching, Germany