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The aim of the present paper was to study the chaotic behavior in a resistor-inductor-diode circuit induced by modulation of voltage amplitude. Time evolutions of the voltage or current signal revealed an extremely chaotic response of the simulated system. These dependences were taken into account in the construction of the phase space. Moreover, based on a bifurcation diagram, the Feigenbaum constant was calculated and verified with reliable and noticeable accuracy.

Current earthquake forecasting approaches are mainly based on probabilistic assumptions, as earthquakes seem to occur randomly. Such apparent randomness can however be caused by deterministic chaos, rendering deterministic short‐term forecasts possible. Due to the short historical and instrumental record of earthquakes, chaos detection has proven challenging, but more frequently occurring slow slip events (SSE) are promising candidates to probe for determinism. Here, we characterize the SSE signatures obtained from GNSS position time series in the Hikurangi Subduction Zone (New Zealand) to investigate whether the seemingly random SSE occurrence is governed by chaotic determinism. We find evidence for deterministic chaos for stations recording shallow SSEs, suggesting that short‐term deterministic forecasting of SSEs, similar to weather forecasts, might indeed be possible over timescales of a few weeks. We anticipate that our findings could open the door for next‐generation SSE forecasting, adding new tools to existing probabilistic approaches. Plain Language Summary Since earthquakes appear to occur randomly, the currently available probabilistic predictions are based on past earthquake records. These predictions estimate the likelihood of an earthquake of a given magnitude occurring within a defined time period. In contrast to such probabilistic approaches, deterministic systems are fully predictable, albeit often confined to short time scales due to their potential chaotic behavior. Probing for deterministic predictability in the earthquake cycle is intractable due to the limited historical instrumental record. However, frequently occurring slow slip events ‐ captured by transient GNSS displacements that can last several weeks ‐ provide a unique opportunity to explore deterministic predictability in these types of slow earthquakes. By studying GNSS time series from various stations on New Zealand’s North Island, we have discovered evidence suggesting that these irregularly occurring slow slip events might be governed by chaotic determinism. This implies the potential to forecast both timing and magnitude of slow slip events a few weeks in advance using deterministic methods, much like we predict weather patterns. Consequently, our theoretical findings could therefore pave the way for innovative approaches to short‐term slow slip forecasting. Key Points Nonlinear analysis of GNSS displacement time series unveils evidence for deterministic chaos in slow slip events in New Zealand Our theoretical findings imply that irregularly occurring slow slip events could potentially be forecasted a few weeks in advance

Iterated quantum protocols with measurement-based selection lead to deterministic chaos for the evolving pure state representing an ensemble of qubits. Deterministic chaos for the pure quantum state may lead to ergodic evolution in the sense that initial states from any small area on the Bloch sphere will cover the whole sphere after a finite number of iterations. We realize two steps of an ergodic protocol in a photonic experiment, where initial qubit states are encoded in the polarization and path degrees of freedom of down-converted photons stemming from a parametric process. We numerically analyze the effect of noise on the time evolution and show that the protocol, described by a Lattès map, remains quasi-ergodic for any initial state if the initial noise is small. Tomographic reconstruction of the quantum states throughout the evolution is consistent with simulations and thus demonstrates ergodicity of the quantum dynamics.

Quantum key distribution (QKD) provides a foundation for information-theoretic security based on quantum mechanics, yet its practical deployment is often constrained by intrinsically low secure key generation rates, particularly in high-bandwidth or low-latency settings. This work introduces a hybrid cryptographic technique that integrates conventional QKD with deterministic chaos, modeled using the Lorenz attractor, to provide a software-based enhancement of the effective key expansion rate. From a short 20-bit QKD seed, the system generates long bitstreams within milliseconds; although these streams exhibit high empirical randomness, their fundamental entropy remains bounded by the seed, consistent with standard cryptographic principles. The method employs the exponential divergence of chaotic trajectories, such that even minute uncertainties in an adversary’s estimate of the initial state lead to rapid desynchronization and, as established in Appendix A, an exponential decay of Eve’s mutual information with respect to the expanded key. Simulation results confirm this theoretical behavior and demonstrate an effective rate amplification exceeding two orders of magnitude over the baseline QKD seed rate. The proposed chaotic expansion operates entirely in software and requires no modifications to existing QKD hardware, offering a practical pathway to enhance throughput for applications ranging from secure video communication to low-latency IoT and edge-computing environments.

This article presents a simplified method for forecasting Poland’s long-term peak electricity demand using a modified Prigogine logistic equation. While complex models like the WEM or PRIMES offer high precision, their complexity and data requirements can be limiting. The proposed model offers a quicker and more accessible alternative, using the average annual load factor (ALF) as a key indicator. Based on historical data (1985–2024), the model was validated and optimized (MAPE < 2%), then applied to forecast the demand through 2040 under three scenarios: coal-based energy, nuclear energy and energy from RESs (renewables). Depending on the scenario, the peak demand is expected to rise from 28.7 GW in 2024 to 34–40 GW in 2040. The model’s strength lies in its ability to capture dynamic system behavior, including chaos and bifurcations, making it suitable for rapid assessments and strategic planning. Despite its limitations—such as a lower level of detail and an inability to integrate sectoral policies—the Prigogine-based approach offers a transparent, cost-effective forecasting tool, especially when complemented by the use of advanced simulation models.

In the search of theoretical models describing cancer, one of promising directions is chaos. It is connected to ideas of “genome chaos” and “life on the edge of chaos”, but they profoundly differ in the meaning of the term “chaos”. To build any coherent models, notions used by both ideas should be firstly brought closer. The hypothesis “life on the edge of chaos” using deterministic chaos has been radically deepened developed in recent years by the discovery of half-chaos. This new view requires a deeper interpretation within the range of the cell and the organism. It has impacts on understanding “chaos” in the term “genome chaos”. This study intends to present such an interpretation on the basis of which such searches will be easier and closer to intuition. We interpret genome chaos as deterministic chaos in a large module of half-chaotic network modeling the cell. We observed such chaotic modules in simulations of evolution controlled by weaker variant of natural selection. We also discuss differences between free and somatic cells in modeling their disturbance using half-chaotic networks.

This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white Gaussian noise source is also sampled regularly to generate random bits. By varying the sampling frequency, and based on the autocorrelation and the approximate entropy analysis of the resulting bit sequences, a comparison is made between bounded chaos, unbounded chaos and Gaussian white noise as an entropy source for random number generators.

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

A dynamical system can often be described in terms of partial differential equations (EDP) or ordinary differential equations (ODE) equations. Moreover, if the long-term dynamic behavior represented in a phase space converges in a disordered way to an attractor, this response is called chaotic. In many cases, it is considered deterministic chaos, i.e., the response follows a unique evolution, which is sensitive to initial conditions, making the behavior difficult or impossible to predict. Such phenomenon can be found in aeroelastic panels, subject to aerodynamic loads and temperature variation, which is the subject of study in this paper. This work address the dynamic analysis of a flat rectangular plate under flutter panel conditions. The system was modeled using Rayleigh-Ritz approximation and the temporal response is obtained using numerical integration by New-Mark method. The dynamic analysis of the system is performed by obtaining the Poincaré plane by Hénon algorithm. Furthermore, using the brute-force search, or exhaustive search, and the Poincaré plane, the bifurcation diagrams were plotted for different pressure and temperature factors. In addition, the 0-1 test for chaos by time series was used to detect the occurrence of non-regular stationary responses. Finally, in the cases of chaos, the Lyapunov exponents were computed using the Sato algorithm. The results showed that the current approach was able to assess the presence or not of deterministic chaos. Furthermore, the results showed how the dynamic pressure and temperature factor affect the dynamic responses.

Background and aims The changing soils is a never-ending process moderated by numerous biotic and abiotic factors. Among these factors, trees may play a critical role in forested landscapes by having a large imprint on soil texture and chemical properties. During their evolution, soils can follow convergent or divergent development pathways, leading to a decrease or an increase in soil spatial complexity. We hypothesized that trees can be a strong local factor intensifying, blocking or modifying pedogenetic processes, leading to local changes in soil complexity (convergence, divergence, or polygenesis). These changes are hypothetically controlled by regionally predominating soil formation processes. Methods To test the main hypothesis, we described the pedomorphological features of soils under tree stumps of fir, beech and hemlock in three soil regions: Haplic Cambisols (Turbacz Reserve, Poland), Entic Podzols (Žofínský Prales Reserve, Czech Republic) and Albic Podzols (Upper Peninsula, Michigan, USA). Soil profiles under the stumps, as well as control profiles on sites currently not occupied by trees, were analyzed in the laboratory for 20 physical and chemical properties. In total, we analyzed 116 soil samples. The age of trees and time of tree death were determined using the radiometry ( 14 C), dendrochronology and repeated tree censuses. To process the data, we used multivariate statistics, namely, redundancy analyses (RDAs) and principal component analyses (PCAs). The statistical significance of variables was tested using Kruskal-Wallis, Dunn, and permutation tests. To reach the main aims of the present study, we examined the dataset at three levels of data complexity: 1) soil regions, 2) microsite (i.e., tree stump versus control site), and 3) soil horizon. Results Living tree roots and empty or infilled root channels were the most important pedogenic factors that affected the dimensions of soil horizons and the moisture in the root zone under tree stumps. Microsites explained almost 6% of the soil variability ( p  < 0.001, F = 13.99), demonstrating that trees significantly impacted soil chemical properties in the root zone in all regions. In the Albic Podzols soil region, we found evidence of “basket” podzolization. Our results suggest the rapid eluviation of organic matter-sesquioxide complexes under the stump, probably leading to local soil divergence in Albic Podzols. However, soil analyses under the stumps in the Haplic Cambisols soil region suggested local polygenetic changes in soils (e.g., hydromorphic processes). The thickness of the A and B horizons increased, and soil chemistry changed under trees in the Entic Podzol soil region compared to the control profiles. Conclusions In addition to regional environmental factors that manifest themselves in regional pedogenesis and that have a key role in modifying the influence of trees on the soil, the tree species can specifically modify pedogenic processes under standing trees. Trees may influence rate of pedogenesis (hemlock in Albic Podzol region) or even soil evolutionary pathways (beech in Haplic Cambisol region).