混沌动力学：2025–2026 年度综述

An annual survey of the nlin.CD arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 120 papers and organised into 44 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• Statistical Equilibria and Turbulence in Fluid Dynamics (12.6%) — Investigates statistical mechanics of 2D turbulence, inverse energy cascades, and finite-size effects in Navier-Stokes and wave turbulence systems.
• Extreme Events and Tipping in Stochastic Systems (12.6%) — Analyzes the prediction, topology, and dynamics of extreme events, rate-induced tipping, and noise-driven transitions in complex dynamical systems.
• Nonlinear Bifurcations and Celestial Mechanics Dynamics (11.9%) — Explores bifurcation structures, periodic orbits, and transport pathways in nonlinear maps, pendulums, and celestial mechanical systems.
• Quantum Chaos and Semiclassical Correspondence (11.6%) — Examines the relationship between classical and quantum chaos, including Lyapunov exponents, out-of-time-order correlators, and dissipative quantum dynamics.
• Data-Driven Modeling and Time Series Analysis (11.3%) — Develops methods for analyzing chaotic time series, including entropy measures, data assimilation, and reduced-order modeling from observational data.
• Lyapunov Exponents and Hamiltonian Chaos Bounds (11.3%) — Focuses on the computation of Lyapunov exponents, chaos bounds in black holes, and integrability versus chaos in Hamiltonian and spin systems.
• Neural Network Dynamics and Learning Systems (8.7%) — Studies the dynamical properties of neural networks, including stability, synchronization, and the application of dynamical systems theory to learning processes.
• Phase Space Structures and Transport Barriers (8.4%) — Analyzes invariant manifolds, fractal basin boundaries, and phase space transport mechanisms in Hamiltonian and coupled oscillator systems.
• Synchronization in Higher-Order Oscillator Networks (7.8%) — Investigates collective dynamics, synchronization, and coupling effects in networks of oscillators, including higher-order interactions and Kuramoto models.
• Reservoir Computing for Nonlinear Prediction (3.7%) — Applies reservoir computing techniques, including physical and quantum implementations, for the prediction and control of nonlinear dynamical systems.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.