Papers

The period of biological and chemical oscillators scales with temperature in a characteristic way. Some oscillators are very well described by an Arrhenius law, while others show systematic deviations. Several frameworks have been proposed to explain such deviations, but they are either phenomenological, focus on activation energy imbalances in specific circuits, or restrict themselves to sequential processes. Here we develop a mechanistic account of the temperature scaling of relaxation oscillators, using the Belousov-Zhabotinsky (BZ) reaction as a model system. We distinguish two typical scenarios by their temperature-scaling signatures. In the first, an Arrhenius-dependent timescale separation parameter produces a biphasic Arrhenius scaling of the period as the oscillator approaches a Hopf bifurcation. In the second, Arrhenius-dependent nullclines hide the same bifurcation behind a canard explosion, yielding apparent single-line Arrhenius scaling. Measuring the electrode potential of a classical and an uncatalyzed BZ reaction, over a very wide temperature range ({\approx} 100 {\deg}C), and comparing to dynamical models, we find that the two reactions represent these two distinct scenarios. Furthermore, we show that a single parameter characterizing the waveform asymmetry between fast and slow phases quantitatively predicts the temperature scaling of three other observables close to the Hopf bifurcation: the period, amplitude, and phase noise. This analysis also recovers elementary activation energies of the BZ mechanism, including a new estimate for the autocatalytic step. We discuss how this framework and its waveform-based diagnostics apply to the analysis of general biochemical relaxation oscillators

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian. A k-nearest-neighbor predictor is trained on trajectory histories, the geometric-mean absolute forecast error is evaluated at phase-consistent horizons, and the exponent is obtained from the slope of the logarithmic error profile. Unlike data-driven approaches that reconstruct local evolution matrices or differentiate a learned surrogate, the proposed method extracts the contraction rate directly from out-of-sample forecast errors. Two adaptations are essential: the forecast step is synchronized with the detected orbit period, and candidate slopes are accepted only when they form a stable consensus across several transient lengths. On the logistic map, the method recovers 92 of 112 negative-exponent parameter values with a mean absolute error of 0.0253 and $R^2=0.886$. On a two-dimensional map without fixed points, independent scalar pipelines based on the three observables $x_n$, $y_n$, and $z_n$ give mean absolute errors of 0.00879–0.01145 and $R^2=0.983$–$0.986$. Because the estimation stage uses only observed trajectories, the framework provides a basis for repeated-relaxation experiments in which short sensor responses are available but the governing equations and analytical Jacobian are unknown. Experimental validation remains a subject of future work.

Magnetic field-line transport in tokamaks is governed by the interplay between chaotic dynamics and invariant phase-space structures that act as partial transport barriers. We investigate the conservative Tokamap, an exact symplectic mapping for magnetic field-line dynamics, using a unified geometrical, dynamical, and statistical framework. Phase-space portraits and Lyapunov exponents characterize the mixed Hamiltonian dynamics, while ensemble-averaged transport exhibits universal dynamic scaling with growth, crossover, and saturation regimes connected through a homogeneous scaling theory. Poincaré recurrence statistics reveal that decreasing the magnetic-shear parameter systematically slows transport, with the characteristic transport time following the algebraic scaling $\tau_c\propto x_q^{-0.213}$. This behavior reflects increasingly dominant stickiness associated with KAM islands, resonance chains, and cantori. Our results establish a direct connection between the geometrical organization of Hamiltonian phase space and macroscopic transport properties, providing a comprehensive framework for understanding long-time magnetic field-line transport in tokamaks and other Hamiltonian systems with mixed phase space.

Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbulent and laminar states coexist. In the lower range, $Re\in (1750,2300)$, turbulence appears in the form of localized traveling structures called "puffs", which form long-lived chaotic dynamical states, whose stochastic decays and splits control the steady state intermittency. At the other end, $Re\in (2300,3000)$, puffs are replaced by an extended turbulent state, with laminar pockets intermittently forming and disappearing within it. Using direct numerical simulations of pipe flow at $Re = 2400, 2450, 2500, 2550$, we provide evidence that these laminar gaps form a distinct dynamical state analogous to puffs: a traveling laminar pocket in a turbulent surrounding, stabilized by a shear-dependent self-tuning mechanism. We analyse the mean spatial profile of these gaps and show that their lifetimes are exponentially distributed, suggesting that gap closing corresponds to an escape from a chaotic saddle. Finally, we suggest these laminar gaps become unstable and disappear at a finite Reynolds number, $Re\sim 2900$, which can be interpreted as the onset point of spatially and temporally homogeneous turbulence.

Although controlling chaos can be regarded as a form of chaos synchronization, conventional chaos synchronization does not provide a practical framework for controlling high-dimensional open chaotic systems, such as weather. In high-dimensional open environmental systems, it is simply impossible to make the difference between drive and response systems asymptotically approach zero over the entire domain. Instead of conventional global chaos synchronization, here I define regional chaos synchronization, in which state variables within only a small target region are synchronized with a target trajectory using actuators located in the target region. Theoretical considerations and numerical experiments show that the performance of regional chaos synchronization is substantially degraded by the injection of errors from exterior regions that the controller is not intended to modify. Even under the same actuator specifications, the performances of regional chaos synchronization differ among trajectories, which is not the case of conventional global chaos synchronization. An appropriate target trajectory differs substantially from the natural trajectory only in the target region. This choice of target trajectories can minimize the injection of errors from exterior regions and thereby enable successful regional chaos synchronization. The implications of this new framework for realistic control problems such as weather control are discussed.

Intermittency represents a fundamental route to chaos in nonlinear dynamical systems. In this work we introduce an adaptive control strategy in which the control parameter of an intermittent system is promoted to a dynamical variable that evolves autonomously under an auxiliary nonlinear map drawn from the same functional hierarchy as the system itself. The construction eliminates the need for orbit identification, local linearization, and trajectory-triggered perturbations, which are central ingredients of conventional feedback schemes. The theoretical framework is developed within a class of one-dimensional nonlinear ergodic maps with exactly known invariant (Sinai–Ruelle–Bowen) measures, for which we derive in closed form (i) the dynamics and invariant measure of the evolving control parameter, (ii) the invariant measure of the coupled system, and (iii) the $q$-generalized Lyapunov exponents before and after control. The generalized Lyapunov spectrum serves as an analytical order parameter for the control process: the collapse of its positive regions provides a quantitative and initial-condition-independent signature of chaos suppression, and yields the sensitivity to initial conditions in explicit form. To establish the physical relevance of the approach beyond low-dimensional maps, we apply the same construction to a cluster of three interacting ultrasound-driven microbubbles described by the Keller–Herring model, promoting the experimentally accessible acoustic driving frequency to a dynamical variable. Systematic bifurcation and Lyapunov analyses, performed over wide ranges of driving pressure, frequency, and equilibrium radii, demonstrate that intermittent chaotic radial oscillations are progressively suppressed and replaced by stable periodic motion.

This paper presents purely convex programs for passively safe impulsive rendezvous and proximity operations in cislunar orbits. Approach, arrival, and abort maneuvers are all designed and validated in the context of maneuver execution error and navigation uncertainty, and formulated for efficient onboard execution in the autonomous scenario. The outlined methods form the baseline onboard guidance routines for NASA's CAPSTONE 02 mission planned to demonstrate autonomous rendezvous and proximity operations capabilities in the southern 9:2 synodic near rectilinear halo orbit. High fidelity closed loop Monte Carlo simulations using the planned relative navigation sensor suite and measurement cadence verify the intended maneuver design performance.

In this paper, we give a memorial tribute to Prof. Erik M. Bollt (1967–2025).

Physical reservoir computing (PRC) leverages the intrinsic dynamics of physical systems to perform information processing while requiring training only in a linear readout layer. Here, we introduce a geometry-programmable metabeam inspired by the hierarchical overlapping architecture of biological scales as a physical reservoir. Contact-mediated interactions between embedded scales induce tunable nonlinear dynamics, enabling controlled transitions between periodic, multi-periodic, and chaotic responses under external excitation. The computational capability of the metabeam reservoir is evaluated using static nonlinear function approximation, Lorenz-63 prediction, and the NARMA-2, NARMA-5, and NARMA-10 benchmarks. Input signals are encoded through the excitation amplitude, whereas computation is realized through the vibrational amplitude of the metabeam followed by a trained linear readout. Across all benchmark tasks, the proposed metabeam consistently outperforms an equivalent linear beam reservoir, yielding lower normalized root-mean-square errors (NRMSEs) and improved computational performance. Different dynamical regimes of the metabeam exhibit distinct computational advantages, with the periodic regime providing the highest prediction accuracy for memory-intensive tasks and the multi-periodic regime achieving the best performance in static nonlinear function approximation. These findings demonstrate that simple interacting surface textures can simultaneously enrich reservoir dynamics and information processing capability, establishing scale-covered metabeams as tunable and mechanically programmable platforms for embodied physical intelligence and PRC.

We investigate the nonlinear dynamics of a thermo-electro-mechanically coupled memristive resonator comprising a doubly clamped Euler–Bernoulli microbeam, an RLC circuit, and a TiO$_2$ memristor with temperature-dependent ionic mobility governed by Mott and Efros–Shklovskii hopping conduction. The dynamics are analyzed using two-dimensional parameter-space maps, bifurcation diagrams, Lyapunov exponents, reconstructed attractors, Poincaré sections, Grassberger–Procaccia correlation-dimension analysis, empirical mode decomposition, the Hilbert–Huang spectrum, and electro-memristive hysteresis. Parameter-space maps reveal predominantly quasi-periodic and deterministic chaotic regimes without stable phase-locked periodic states. Bifurcation analyses show that the beam length and excitation frequency govern the dynamics through the frequency ratio $r_\omega=\omega_0/\omega_b$, whereas the excitation current mainly controls the oscillation amplitude and chaotic intensity. Under fixed operating conditions, the asymptotic regime depends on the initial conditions, and complementary diagnostics identify the thermo-memristive subsystem as the primary source of the nonlinear complexity, subsequently transmitted to the microbeam through electromechanical coupling. Temperature continuously reorganizes the electro-memristive hysteresis through the chain $T \to \sigma(T) \to M(w,T) \to i_m(t) \to w(t)$. The hysteresis area evolves non-monotonically with temperature, revealing a configuration-dependent optimal thermo-memristive operating point. These findings highlight temperature, beam length, and electrical excitation as complementary control parameters for tailoring thermo-memristive memory, deterministic chaos, and nonlinear dynamics in thermo-active MEMS, with potential applications in neuromorphic sensing and chaos-based secure communication.

We present the first demonstration of transition to spatiotemporal chaos with multiple colliding pulse sequences in systems described by perturbed cubic nonlinear Schrödinger (NLS) equations. For this purpose, we consider propagation of multiple sequences of optical pulses in two distinct types of nonlinear waveguide arrays with cubic gain and loss. By employing a perturbation theory for NLS solitons, we show that the dynamics of pulse energies in the waveguide array systems is described by generalized Lotka-Volterra (LV) models, which exhibit dissipative chaos in a wide region in parameter space. We test the LV models' predictions for chaotic dynamics of pulse energies by extensive numerical simulations with perturbed systems of coupled-NLS equations. We find excellent agreement between the results of the LV and coupled-NLS models for energy dynamics in both types of waveguide array systems, despite the strong pulse pattern distortions and the strongly nonlinear nature of the dynamics.

Universal hallmarks of quantum chaos—such as the ramp and plateau in the spectral form factor—and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~\cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models—including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons—can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-$N$ limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in $1/N^2$. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects—such as baby-universe and wormhole condensates—which yield double exponential effects in $G_N$. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.

The influence of the time-delay parameters on the bifurcations of "non-classical" maximal attractors in the Sommerfeld-Kononenko non-ideal dynamical system "spherical pendulum-electric motor" is investigated. Regular and chaotic maximal attractors of this system, as well as their bifurcations, are described. It is established that the presence of time delays can fundamentally change the type of limit sets of the considered dynamical system and significantly alter the scenarios of transitions to deterministic chaos.