Chaotic Dynamics
Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
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System-label and parameter-control channels let a reservoir computer generalize from partial data to full diagrams
· “Inferring bifurcation diagrams of two distinct chaotic systems by a single machine”
Global linear stability on the time-averaged flow predicts neutrality for a mode that actually grows.
· “Lyapunov stability analysis of the chaotic flow past two square cylinders”
Voigt-regularised turbulence shows an energy bump built from two equilibrium ranges, not pure dissipation.
· “Dynamical slowdown, bottlenecks, and multiscaling in Voigt-regularised turbulence”
If it works, the NMI-H plane separates regular, chaotic and noisy series and adds directionality without transfer entropy.
· “Mutual information-entropy plane: a new quantifier space for time series analysis”
A framework using structured stochastic liftings, delay windows, and state-space enrichment to detect and repair non-closure in probability…
· “Identifying Probability Localization Dynamics via Structured Stochastic Liftings”
Early info-loss and late thermalization rates follow from energy-dependent formulas for GOE, GUE, GβE, and regular graphs.
· “Characterization of Chaotic Evolution in Quantum Systems Induced by Random Hermitian Matrices”
New theorem ties noise to an order: noisy signals look more random, and the noise level can be bounded without fitting.
· “Noise Effects on Ordinal Pattern Statistics via Majorization”
Chaotic synchronization plus a measurement-dependent wave field keeps CHSH correlations above 2 even after coupling is switched off.
· “Synchronization induces Bell violations in a model of walking droplets”
Front speed grows as the square root of the reduced Rayleigh number; roll spacing shifts from linear to quarter-power.
· “Propagating fronts of convection rolls in Rayleigh-B\'enard convection”
Entangling power proves the gap in the kicked Ising chain; two-qubit gates miss the Haar value.
Finite noisy oscillator ensembles yield exponents whose sum satisfies the Rushbrooke inequality.
From one 20,000-step trajectory, centrality patterns expose stable and unstable periodic points, supertracks, and crisis boundaries.
· “Identifying the structure of dynamical transitions in logistic map”
Same forecasting protocol on four wave experiments shows frequency-selective turbulence instability.
· “Data-Driven Characterisation of Wave-Forced Turbulence Using Time-Resolved Forecast-Error Growth”
A single projection recipe gives explicit Jacobi and Riemann theta wave functions for wells and Coxeter billiards.
· “Coherent states in quantum billiards constructed in the basis of the continued eigenfunctions”
A flux-over-saddle formula gives the mean flip rate at any energy, with chaotic trajectories matching at the few-percent level.
Reservoir computing isolates why the multi-model mean beats its members: errors cancel along the unstable manifold of chaos.
· “Understanding the superiority of multi-model ensemble forecasts through reservoir computing”
Varying only the mean and amplitude of interaction delays produces abrupt, fractal changes in global flocking order.
· “Intermittent Flocking and Fractal Collective Order Induced by Time-Varying Delays”
Manifold crossings appear where the state is periodic and vanish where it is chaotic.
Treating each archive on its own timescale lifts 300–2000 m ocean heat content agreement from CE 0.19 to 0.91.
· “Coupled multiscale paleoclimate reconstruction with four-dimensional variational data assimilation”
A coarse grid, a Markov chain, and a filter expose ordered epochs inside chaotic dynamics—no trajectory inspection required.
· “Set-Oriented Approach to the Analysis of Chaotic Itinerancy”
A single Lipschitz bound replaces matrix-inequality solvers and cuts path computations from quadratic to O(n^3)
· “A (Purely) Graph-Theoretic Approach to Synchronization of Nonlinear Dynamical Networks”
One Posit library matches fp64's precision but runs ~1000x slower; the other errs ~10x more.
At 100,000 points, one float32 record gives λ≈0.0016 while restarts give 0.6917, close to ln2.
The paper separates the noise partition function from the dynamics, turning chaos into spontaneous supersymmetry breaking.
Hovering, oscillation, and runaway share one delayed feedback loop; saturation, not lost stability, sets the escape switch.
· “An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent”
A spanning acyclic backbone plus a small restoring weight yields full eigenmode decoupling.
· “Positive Arc-Weight Design Makes Every Directed Laplacian Diagonalizable”
Shell-model numerics and proofs find one long-time decay rate for any positive diffusivity; κ sets only the prefactor.
· “Long-time behavior of optimal mixing in an advection-diffusion shell model”
Two structural coefficients keep pairwise and triangular couplings separate while matching steady-state branches and transitions.
A single finite-time measurement on initial states certifies equilibrium for almost all states and times.
· “Aperiodicity is sufficient for macroscopic thermalization”
A nearly invisible single-spin tilt flips half the moiré domains; every quench draws an independent random pattern.
· “Emergence of moir\'e magnetic chaos in twisted bilayer CrI3”
Group interactions collapse into one effective coupling that reproduces full-network transitions.
A delayed Lotka-Volterra model places real charts at peak unpredictability, explaining the log-normal-to-power-law shift.
· “Maximally chaotic competition for attention in the cultural domain”
Generalized equipartition and a generating functional match simulations where random-phase approximations break down.
· “Equilibrium Distributions for Strongly Nonlinear Many-Body Systems”
Bloch-sphere spreading, read with Wasserstein distance, turns sensitivity and coverage into two clean diagnostics.
Exact spectrum for the q=3 kicked Potts chain gives every Rényi entropy S(t)=min(2t,N) log 3 until saturation.
· “Spread of Entanglement in Generalized Kicked Ising Chain”
Even a tiny rope mass turns the mass-ratio-3 integrable case into chaos.
A reservoir computer predicts each next change; a squared correlation above 0.5 labels the series chaotic.
· “Learning a quantitative criterion for distinguishing chaos from noise”
The falling-to-rising phase ratio sets the period, amplitude, and phase noise over a 100-degree range.
US and French name-frequency curves stay stable for 100+ years, with Gini 0.85–0.95, fitting Rayleigh-Jeans condensation.
· “Thermodynamic statistics of given names in USA and France”
Nearest-neighbor forecast-error decay gives contraction rates from short recovery responses, without a Jacobian.
Lower magnetic shear traps trajectories longer near islands and cantori, slowing return times.
· “A Symplectic Map Approach to Magnetic Field-Line Dynamics in Tokamaks”
Self-tuning laminar pockets persist for exponentially distributed lifetimes, then vanish near Re=2900.
A control-window formula shows trajectory choice matters as much as actuator design for weather-scale systems.
· “Regional Chaos Synchronization towards controlling high-dimensional open environmental systems”
An exact instability measure shows the collapse, and three-bubble simulations confirm stable periodic motion returns.
A single fixed-time convex program handles approach, arrival, and abort maneuvers for the CAPSTONE 02 lunar mission.
· “Passively Safe Convex Guidance for Cislunar Rendezvous and Proximity Operations”
A tribute from family and colleagues gathers his contributions to chaos control, data-driven modeling, and mentorship.
Scale contact yields tunable dynamics; periodic motion is best for memory tasks, multi-periodic for static maps.
· “Emergent Physical Intelligence in Biomimetic Scale Metabeams”
Peak hysteresis area appears near 407 K, offering a thermal design rule for chaos-based devices.
· “Thermal Control of Hysteresis and Deterministic Chaos in a Memristive MEMS Resonator”
Shifted energy variables keep the reduced model valid despite distorted pulse shapes, matching full simulations over long distances.
A smooth filter extracts random-matrix universality from one chaotic spectrum, with wormholes as its gravity dual.
· “Ramp, Plateau, and Wormholes without Averaging, and Hyper-non-perturbative Structures in Gravity”
At delays near 7e-4, a chaotic maximal attractor becomes a periodic family, then period-doubles into new chaos.
In a delayed Duffing pair the coupling acts as a bias that sets where the response's high, sharp band appears.
· “Interplay of coupling and forcing: Coherence in a nonlinear delayed oscillator”
Driver-induced dissipation peaks exactly where a swarm predicts chaos best, offering a training-free diagnostic.
· “Entropy production of active matter systems as indicator for computing performance”
Series-coupled RTDs use symmetry-breaking to hold three stable states; a single current pulse selects any one.
· “Multistability and state-switching in series-coupled resonant tunneling diodes”
It predicts the breakup of invariant tori and chaos growth at unseen controls, trained only on regular motion.
· “Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks”
New force-aligned and orbit-aligned sections beat rigid cuts at exposing hidden islands in the elastic pendulum.
No pairwise links needed: an exact threshold and circular orbits in the complex plane mark the onset
· “Breathing chimera states from purely triadic interactions”
Small prompt changes stay hidden, then abruptly flip outputs, mimicking chaotic attractors.
· “Chaos in reason: How chain-of-thought LLMs can look for an answer”
Biot–Savart filtering of high vorticity flattens the bottleneck and drives structure functions toward p/3
One shared FM signal splits three identical uncoupled oscillators into a synchronized pair and a loner
Each resonant frequency births a stable motion that unravels via grazing, saddle-node, then period-doubling into chaos.
· “Grazing bifurcations of linear impact oscillators in the zero damping limit”
Correlation-matrix spectra act as empirical order parameters without a free energy or pre-chosen macroscopic variable.
A single growth-rate curve shows why refining initial data cannot save high-Re forecasts
· “The real butterfly effect: from the pop culture to mathematics and physics”
Payoff ties at invaders, pairs, stripes and cores bound sustained chaos across densities
Sublevel persistence plus simple classifiers match Lyapunov transitions on Duffing, Rössler, and Lorenz.
About one run in four recovers a family absent from training; the data, not the init scheme, steers which
Chaotic time-series prediction stays accurate at NMSE < 0.1 while per-sample energy drops from 237 to 22 pJ.
· “Approximate reservoir computing with a semiconductor laser for reducing energy consumption”
In a 1024-node SLM reservoir, rewiring near p = 0.05–0.2 gives the best memory and prediction.
Re-analysis of a published wave-equation study shows Lyapunov exponents near zero and closed invariant curves.
Rulkov pair in 4D stays bounded and chaotic; simulation shows a strange attractor, dimension near 1.8.
Quantum and optical resonance norms reduce to surface integrals, with factor-2 corrections for spheres and disks.
· “Norm of resonance states in quantum scattering and electromagnetic systems”
An order-statistics formula matches simulations over decades and predicts exponential survival even at strong coupling.
· “Multiplicity of Stable Attractors in Disordered Neural Models”
A single dynamical regime unites universal approximation and near-optimal representation geometry.
· “Driven criticality links universal computation and optimal representations”
A kicked-rotor quantum battery stores energy as τ² and stays nearly fully extractable, even with strong entanglement.
· “Quantum resonance-enhanced performance of quantum battery”
In an open biased walk, each starting distribution picks its own quasi-stationary state and decay rate.
· “Quasi-stationary and quasi-ergodic distributions in the Pelikan random map”
Proof: with at least one finite rod, only total energy and center-of-mass energy survive as analytic invariants.
· “Absence of hidden analytic conserved quantities in harmonically confined rods”
A dominant complex resonance pair sets the period and lifetime of statistical periodicity—independent of Lyapunov stability.
· “Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances”
A pre-run number tells whether SINDy or PySR can recover a system, and why deeper chaos isn't always better.
· “Attractor Geometry Determines the Identifiability Limits of System Discovery”
A three-level model finds mid-chain infection causes oscillations; apex infection causes top-predator extinction.
· “Gravity-Driven Eco-Epidemiological Dynamics in Tri-Trophic Food Chains”
In 2D magnetoconvection, a vertical field turns periodic rolls into chaotic traveling rolls via saddle-focus collisions and reconnection.
