Search Results (247)

With the rapid proliferation of real-time digital communication, particularly in multimedia applications, securing transmitted image data has become a vital concern. While chaotic systems have shown strong potential for cryptographic use, most existing approaches rely on low-dimensional, integer-order architectures, limiting their complexity and resistance to attacks. Advances in fractional calculus and memristive technologies offer new avenues for enhancing security through more complex and tunable dynamics. However, the practical deployment of high-dimensional fractional-order memristive chaotic systems in hardware remains underexplored. This study addresses this gap by presenting a secure image transmission system implemented on a field-programmable gate array (FPGA) using a universal high-dimensional memristive chaotic topology with arbitrary-order dynamics. The design leverages four- and five-dimensional hyperchaotic oscillators, analyzed through bifurcation diagrams and Lyapunov exponents. To enable efficient hardware realization, the chaotic dynamics are approximated using the explicit fractional-order Runge–Kutta (EFORK) method with the Caputo fractional derivative, implemented in VHDL. Deployed on the Xilinx Artix-7 AC701 platform, synchronized master–slave chaotic generators drive a multi-stage stream cipher. This encryption process supports both RGB and grayscale images. Evaluation shows strong cryptographic properties: correlation of $-6.1081\times {10}^{-5}$, entropy of 7.9991, NPCR of 99.9776%, UACI of 33.4154%, and a key space of $2^{1344}$, confirming high security and robustness. Full article

Span-wise homogeneous supersonic cavity flows display complicated structures due to shear layer breakdown, flow acoustic resonance, and even non-linear hydrodynamic-acoustic interactions. In practical applications, such as aircraft bays, the cavity is of finite width and has doors, both of which introduce distinctive phenomena that couple with the shear layer at the cavity lip, further modulating shear layer bifurcations and tonal mechanisms. In particular, asymmetric states manifest as ‘tornado’ vortices with significant practical consequences on the design and operation. Both inward- and outward-facing leading-wedge doors, resulting in leading edge shocks directed into and away from the cavity, are examined at select opening angles ranging from $22.5°$ to $90°$ (fully open) at Mach 1.6. The computational approach utilizes the Reynolds-Averaged Navier–Stokes equations with a one-equation model and is augmented by experimental observations of cavity floor pressure and surface oil-flow patterns. For the no-doors configuration, the asymmetric results are consistent with a long-time series DDES simulation, previously validated with two experimental databases. When fully open, outer wedge doors (OWD) yield an asymmetric flow, while inner wedge doors (IWD) display only mildly asymmetric behavior. At lower door angles (partially closed cavity), both types of doors display a successive bifurcation of the shear layer, ultimately resulting in a symmetric flow. IWD tend to promote symmetry for all angles observed, with the shear layer experiencing a pitchfork bifurcation at the ‘critical angle’ ($67.5°$). This is also true for the OWD at the ‘critical angle’ ($45°$), though an entirely different symmetric flow field is established. The first observation of pitchfork bifurcations (‘critical angle’) for the IWD is at $67.5°$ and for the OWD, $45°$, complementing experimental observations. The back wall signature of the bifurcated shear layer (impingement preference) was found to be indicative of the 3D cavity dynamics and may be used to establish a correspondence between 3D cavity dynamics and the shear layer. Below the critical angle, the symmetric flow field is comprised of counter-rotating vortex pairs at the front and back wall corners. The existence of a critical angle and the process of door opening versus closing indicate the possibility of hysteresis, a preliminary discussion of which is presented. Full article

The importance of chaotic systems as the main pseudo-random cryptographic generator of encryption algorithms in the field of communication secrecy cannot be overstated, but in practical applications, researchers often choose to build upon traditional chaotic maps, such as the logistic map, for study and application. This approach provides attackers with more opportunities to compromise the encryption scheme. Therefore, based on previous results, this paper theoretically investigates discrete chaotic mappings in the real domain, constructs a general method for a class of quadratic chaotic mappings, and justifies its existence based on a robust chaos determination theorem for S single-peaked mappings. Based on the theorem, we construct two chaotic map examples and conduct detailed analysis of their Lyapunov exponent spectra and bifurcation diagrams. Subsequently, comparative analysis is performed between the proposed quadratic chaotic maps and the conventional logistic map using the 0–1 test for chaos and SE complexity metrics, validating their enhanced chaotic properties. Full article

This study develops a dynamic IS-LM macroeconomic model that incorporates delayed taxation and a memory-dependent income effect, and calibrates it to quarterly data for Romania (2000–2023). Within this framework, fiscal policy lags are modelled using a “memory” income variable that weights past incomes, an approach grounded in distributed lag theory to capture how historical economic conditions influence current dynamics. The model is analysed both analytically and through numerical simulations. We derive stability conditions and employ bifurcation analysis to explore how the timing of taxation influences macroeconomic equilibrium. The findings reveal that an immediate taxation regime yields a stable adjustment toward a unique equilibrium, consistent with classical IS-LM expectations. In contrast, delayed taxation, where tax revenue depends on past income, can destabilise the system, giving rise to cycles and even chaotic fluctuations for parameter values that would be stable under immediate collection. In particular, delays act as a destabilising force, lowering the threshold of the output-adjustment speed at which oscillations emerge. These results highlight the critical importance of policy timing: prompt fiscal feedback tends to stabilise the economy, whereas lags in fiscal intervention can induce endogenous cycles. The analysis offers policy-relevant insights, suggesting that reducing fiscal response delays or counteracting them with other stabilisation tools is crucial for macroeconomic stability. Full article

Background/Objective: Precise aneurysm volume measurement offers a transformative edge for risk assessment and treatment planning in clinical settings. Currently, clinical assessments rely heavily on manual review of medical imaging, a process that is time-consuming and prone to inter-observer variability. The widely accepted standard of care primarily focuses on measuring aneurysm diameter at its widest point, providing a limited perspective on aneurysm morphology and lacking efficient methods to measure aneurysm volumes. Yet, volume measurement can offer deeper insight into aneurysm progression and severity. In this study, we propose an automated approach that leverages the strengths of pre-trained neural networks and expert systems to delineate aneurysm boundaries and compute volumes on an unannotated dataset from 60 patients. The dataset includes slice-level start/end annotations for aneurysm but no pixel-wise aorta segmentations. Method: Our method utilizes a pre-trained UNet to automatically locate the aorta, employs SAM2 to track the aorta through vascular irregularities such as aneurysms down to the iliac bifurcation, and finally uses a Long Short-Term Memory (LSTM) network or expert system to identify the beginning and end points of the aneurysm within the aorta. Results: Despite no manual aorta segmentation, our approach achieves promising accuracy, predicting the aneurysm start point with an R² score of 71%, the end point with an R² score of 76%, and the volume with an R² score of 92%. Conclusions: This technique has the potential to facilitate large-scale aneurysm analysis and improve clinical decision-making by reducing dependence on annotated datasets. Full article

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. Full article

This paper introduces and analyzes a novel fractional-order Ananthakrishna model. The stability of its equilibrium points is first investigated using fractional-order stability criteria, particularly in regions where the corresponding integer-order model exhibits instability. A linear finite difference scheme is then developed, incorporating an accelerated L1 method for the fractional derivative. This enables a detailed exploration of the model’s dynamic behavior in both the time domain and phase plane. Numerical simulations, including Lyapunov exponents, bifurcation diagrams, phase and time diagrams, demonstrate that the fractional model exhibits stable and periodic behaviors across various fractional orders. Notably, as the fractional order approaches a critical threshold, the time required to reach stability increases significantly, highlighting complex stability-transition dynamics. The computational efficiency of the proposed scheme is also validated, showing linear CPU time scaling with respect to the number of time steps, compared to the nearly quadratic growth of the classical L1 and Grünwald-Letnikow schemes, making it more suitable for long-term simulations of complex fractional-order models. Finally, four types of stress-time curves are simulated based on the fractional Ananthakrishna model, corresponding to both stable and unstable domains, effectively capturing and interpreting experimentally observed repeated yielding phenomena. Full article

Fractional calculus plays a central role in modeling memory-dependent processes and complex dynamics across various fields, including control theory, fluid mechanics, and bioengineering. This study introduces an efficient and stable fractional-order iterative method based on the Caputo derivative for solving nonlinear equations. By employing a Taylor series expansion, a local convergence analysis shows that for $\gamma \in (0,1]$, the method achieves a convergence order of $2\gamma +1$. To address challenges related to memory effects and instability in existing approaches, the proposed scheme incorporates parameter optimization through chaos and bifurcation analysis. Dynamical plane analysis reveals that parameter values within chaotic regimes lead to divergence, while those in stable regions converge uniformly. The method’s performance is evaluated using a set of nonlinear models drawn from biomedical engineering, including enzyme kinetics with inhibition, extended glucose–insulin regulation, drug dose–responses, and lung volume–pressure dynamics. Comparative results demonstrate that the proposed approach outperforms existing methods in terms of iteration count, residual error, CPU time, convergence order, fractal behavior, and memory efficiency. These findings underscore the method’s applicability to complex systems characterized by nonlinearity and memory effects in scientific and engineering contexts. Full article

The generation of road interchange networks benefits various applications, such as vehicle navigation and intelligent transportation systems. Traditional methods often focus on common road structures but fail to fully utilize long-term trajectory continuity and flow information, leading to fragmented results and misidentification of overlapping roads as intersections. To address these limitations, we propose a forward and reverse tracking method for high-accuracy road interchange network generation. First, raw crowdsourced trajectory data is preprocessed by filtering out non-interchange trajectories and removing abnormal data based on both static and dynamic characteristics of the trajectories. Next, road subgraphs are extracted by identifying potential transition nodes, which are verified using directional and distribution information. Trajectory bifurcation is then performed at these nodes. Finally, a two-stage fusion process combines forward and reverse tracking results to produce a geometrically complete and topologically accurate road interchange network. Experiments using crowdsourced trajectory data from Shenzhen demonstrated highly accurate results, with 95.26% precision in geometric road network alignment and 90.06% accuracy in representing the connectivity of road interchange structures. Compared to existing methods, our approach enhanced accuracy in spatial alignment by 13.3% and improved the correctness of structural connections by 12.1%. The approach demonstrates strong performance across different types of interchanges, including cloverleaf, turbo, and trumpet interchanges. Full article

In a biological nervous system, neurons are connected to each other via synapses to transmit information. Synaptic crosstalk is the phenomenon of mutual interference or interaction of neighboring synapses between neurons. This phenomenon is prevalent in biological neural networks and has an important impact on the function and information processing of the neural system. In order to simulate and study this phenomenon, this paper proposes a memristor model based on hyperbolic tangent function for simulating the activation function of neurons, and constructs a three-neuron HNN model by coupling two memristors, which brings it close to the real behavior of biological neural networks, and provides a new tool for studying complex neural dynamics. The intricate nonlinear dynamics of the MHNN are examined using techniques like Lyapunov exponent analysis and bifurcation diagrams. The viability of the MHNN is confirmed through both analog circuit simulation and FPGA implementation. Moreover, an image encryption approach based on the chaotic system and a dynamic key generation mechanism are presented, highlighting the potential of the MHNN for real-world applications. The histogram shows that the encryption algorithm is effective in destroying the features of the original image. According to the sensitivity analysis, the bit change rate of the key is close to 50% when small perturbations are applied to each of the three parameters of the system, indicating that the system is highly resistant to differential attacks. The findings indicate that the MHNN displays a wide range of dynamical behaviors and high sensitivity to initial conditions, making it well-suited for applications in neuromorphic computing and information security. Full article

This study numerically investigates unsteady natural convection (NC) heat transfer (HT) and entropy generation (E_gen) in trapezoidal cavities filled with two thermally stratified fluids. Both air-filled and water-filled configurations are analyzed to evaluate and compare their thermal performance under varying conditions. The cavities are characterized by a heated base, thermally stratified sloped walls, and a cooled top wall. The governing equations are numerically solved using the finite volume (FV) approach. The study considers a Prandtl number (Pr) of 0.71 for air and 7.01 for water, Rayleigh numbers (Ra) ranging from 10³ to 5 × 10⁷, and an aspect ratio (AR) of 0.5. Flow behavior is examined through various parameters, including temperature time series (TTS), average Nusselt number (Nu), average entropy generation (E_avg), average Bejan number (Be_avg), and ecological coefficient of performance (ECOP). Three bifurcations are identified during the transition from steady to chaotic flow for both fluids. The first is a pitchfork bifurcation, occurring between Ra = 10⁵ and 2 × 10⁵ for air, and between Ra = 9 × 10⁴ and 10⁵ for water. The second, a Hopf bifurcation, is observed between Ra = 4.7 × 10⁵ and 4.8 × 10⁵ for air, and between Ra = 10⁵ and 2 × 10⁵ for water. The third bifurcation marks the onset of chaotic flow, occurring between Ra = 3 × 10⁷ and 4 × 10⁷ for air, and between Ra = 4 × 10⁵ and 5 × 10⁵ for water. At Ra = 10⁶, the average HT in the air-filled cavity is 85.35% higher than in the water-filled cavity, while E_avg is 94.54% greater in the air-filled cavity compared to water-filled cavity. At Ra = 10⁶, the thermal performance of the cavity filled with water is 4.96% better than that of the air-filled cavity. These findings provide valuable insights for optimizing thermal systems using trapezoidal cavities and varying working fluids. Full article

Background: Severe neonatal Ebstein’s anomaly (EA) is associated with a high risk of mortality. A new therapeutic approach aims to combine the advantages of Starnes’ procedure in stabilizing critically ill neonates with the long-term superiority of biventricular physiology after cone reconstruction. Case report: The echocardiography of a male preterm (36 weeks’ gestation; birth weight 2400 g) demonstrated EA Carpentier type C, membranous pulmonary atresia, and hypoplastic pulmonary arteries (PAs). After undergoing the Starnes procedure postnatally, multiple dilatations of the AP shunt and the Starnes fenestration followed. Cone reconstruction was performed at 15 months of age. Surgical revision addressed tricuspid and pulmonary valve insufficiency and PA bifurcation stenosis. Subsequently, PA branch stenosis with severe impairment of right ventricular function and dilatation required stent implantation. At the last follow-up, at 3 years of age, the patient was asymptomatic with sufficient exercise tolerance. Discussion: The American Association for Thoracic Surgery recently recommended evaluating all Starnes patients for potential conversion to cone. Consequently, the Starnes procedure should be modified to facilitate subsequent biventricular correction. Both the optimal timing of conversion and the appropriate assessment to reliably evaluate feasibility and the prospects for success require further investigation. Conclusions: Conversion from Starnes to cone is technically feasible, even in cases of severe EA, prematurity, low birth weight, and additional cardiac comorbidities, and provides promising initial results. Further research is needed to define candidacy and the optimal timing of conversion, and to assess long-term outcomes. The high therapeutic effort and complexity make this treatment approach suitable only for quaternary centers. Full article

After linear differential systems in the plane, the easiest systems are quadratic polynomial differential systems in the plane. Due to their nonlinearity and their many applications, these systems have been studied by many authors. Such quadratic polynomial differential systems have been divided into ten families. Here, for two of these families, we classify all topologically distinct phase portraits in the Poincaré disc. These two families have already been studied previously, but several mistakes made there are repaired here thanks to the use of a more powerful technique. This new technique uses the invariant theory developed by the Sibirskii School, applied to differential systems, which allows to determine all the algebraic bifurcations in a relatively easy way. Even though the goal of obtaining all the phase portraits of quadratic systems for each of the ten families is not achievable using only this method, the coordination of different approaches may help us reach this goal. Full article

The journal bearing, a critical component of the rotating shaft, is influenced by various factors including friction, wear, and heat effects under actual working conditions. This study developed an advanced approach for optimizing the performance of journal bearings with surface texture. This approach allows for finding the influences of bearing parameters such as journal clearance, rotational speed, and shaft eccentricity ratio on the optimization results. The results show that whether under smaller journal clearances, higher rotational speeds, or larger shaft eccentricity ratios, the formation of intricate bifurcation patterns and enhanced branching in surface textures is consistently promoted. The optimized texture’s shape leads to a reduction in texture depth while significantly improving both the load-carrying capacity (LCC) and oil film thickness. This approach precisely determines the spatial and depth characteristics of texture elements, ensuring their optimal placement and geometry, and offers valuable insights and directions for future research. Full article

This paper presents and examines a discrete-time predator–prey model of the Leslie type, integrating a Holling type IV functional response for analysis. The mathematical analysis succinctly identifies fixed points and evaluates their local stability within the model. The study employs the normal form approach and bifurcation theory to explore codimension-one and two bifurcation behaviors for this model. The primary conclusions are substantiated by a combination of rigorous theoretical analysis and meticulous computational simulations. Additionally, utilizing fractal basin boundaries, periodicity variations, and Lyapunov exponent distributions within two-parameter spaces, we observe a mode-locking structure akin to Arnold tongues. These periods are arranged in a Farey tree sequence and embedded within quasi-periodic/chaotic regions. These findings enhance comprehension of bifurcation cascade emergence and structural patterns in diverse biological systems with discrete dynamics. Full article