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20 pages, 2130 KB  
Article
Valorizing Pruning Residues into Biochar for Remediating Acidified Cropland Soil: Effects on Fertility, Enzymes, and Bacterial Communities
by Haowen Li, Yingmei Huang, Juntao Zhang, Yongxin Liang, Jialong Wu and Kexing Liu
Agronomy 2026, 16(3), 296; https://doi.org/10.3390/agronomy16030296 (registering DOI) - 24 Jan 2026
Abstract
Intensive agriculture has intensified soil acidification in southern China, threatening crop productivity and ecosystem sustainability. Biochar can neutralize acidity, improve pH buffering, and enhance nutrient retention and microbial habitat in acidic soils. Accordingly, we produced biochars from pruned eucalyptus (ABC), camphora (ZBC), and [...] Read more.
Intensive agriculture has intensified soil acidification in southern China, threatening crop productivity and ecosystem sustainability. Biochar can neutralize acidity, improve pH buffering, and enhance nutrient retention and microbial habitat in acidic soils. Accordingly, we produced biochars from pruned eucalyptus (ABC), camphora (ZBC), and guava (FBC) branches via pyrolysis at 500 °C. The three biochars were characterized by elemental analysis, Fourier Transform Infrared Spectroscopy (FTIR), and SEM (Scanning Electron Microscopy), and their effects on soil properties, enzyme activities, and bacterial communities were evaluated through a 56-day incubation experiment in an acidified, continuously cropped soil. Physicochemical characterization revealed that ZBC and FBC possessed more oxygen-containing functional groups and greater potential for pH buffering and nutrient release, whereas ABC exhibited higher aromaticity and structural stability. Biochar significantly increased soil pH by 0.62–1.42 units and improved nutrient availability and carbon pools (p < 0.05). Additionally, 4% ZBC increased urease and sucrase activities by 21.54% and 79.34%, respectively, while 2% FBC increased cellulase activity by 25.99%. High-throughput sequencing identified Acidobacteria and Proteobacteria as the dominant phyla; ZBC and FBC at 0.5% and 2% significantly increased Shannon and Chao1 indices. Redundancy analysis indicated that available potassium, pH, soil organic carbon, urease, sucrase, and cellulase were the primary drivers of bacterial community variation and positively associated with carbon-cycling phyla. These findings demonstrate that feedstock-specific biochar properties critically regulate soil biogeochemical processes, offering a sustainable strategy to remediate acidified soils and valorize agroforestry residues. Full article
(This article belongs to the Section Soil and Plant Nutrition)
18 pages, 2758 KB  
Article
Synergistic Effects of Coal Gasification Slag-Based Soil Conditioner and Vermicompost on Soil–Microbe–Plant Systems Under Saline–Alkali Stress
by Hang Yang, Longfei Kang, Qing Liu, Qiang Li, Feng Ai, Kaiyu Zhang, Xinzhao Zhao and Kailang Ding
Sustainability 2026, 18(3), 1180; https://doi.org/10.3390/su18031180 - 23 Jan 2026
Abstract
Soil salinization remains a critical constraint on global land sustainability, severely limiting agricultural output and ecosystem resilience. To address this issue, a field trial was implemented to investigate the interactive benefits of vermicompost (VC) and a novel soil conditioner derived from coal gasification [...] Read more.
Soil salinization remains a critical constraint on global land sustainability, severely limiting agricultural output and ecosystem resilience. To address this issue, a field trial was implemented to investigate the interactive benefits of vermicompost (VC) and a novel soil conditioner derived from coal gasification slag-based soil conditioner (CGSS) in mitigating saline–alkali stress. The perennial forage grass Leymus chinensis, valued for its ecological robustness and economic potential under adverse soil conditions, served as the test species. Five treatments were established: CK (unamended), T1 (CGSS alone), T2 (VC alone), T3 (CGSS:VC = 1:1), T4 (CGSS:VC = 1:2), and T5 (CGSS:VC = 2:1). Study results indicate that the combined application of CGSS and VC outperformed individual amendments, with the T4 treatment demonstrating the most effective results. Compared to CK, T4 reduced soil electrical conductivity (EC) by 12.00% and pH by 5.17% (p < 0.05), while markedly enhancing key fertility indicators—including soil organic matter and the availability of nitrogen, phosphorus, and potassium. Thus, these improvements translated into superior growth of L. chinensis, reflected in significantly greater dry biomass, expanded leaf area, and increased plant height. Additionally, the T4 treatment increased soil microbial richness (Chao1 index) by 21.5% and elevated the relative abundance of the Acidobacteria functional group by 16.9% (p < 0.05). Hence, T4 treatment (CGSS: 15,000 kg·ha−1; VC: 30,000 kg·ha−1) was identified as the optimal remediation strategy through a fuzzy comprehensive evaluation that integrated multiple soil and plant indicators. From an economic perspective, the T4 treatment (corresponding to a VC-CGSS application ratio of 2: 1) exhibits a lower cost compared to other similar soil conditioners and organic fertilizer combinations for saline–alkali soil remediation. This study not only offers a practical and economically viable approach for reclaiming degraded saline–alkali soils but also advances the circular utilization of coal-based solid waste. Furthermore, it deepens our understanding of how integrated soil amendments modulate the soil–microbe–plant nexus under abiotic stress. Full article
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13 pages, 783 KB  
Article
Some New Maximally Chaotic Discrete Maps
by Hyojeong Choi, Gangsan Kim, Hong-Yeop Song, Sangung Shin, Chulho Lee and Hongjun Noh
Entropy 2026, 28(1), 131; https://doi.org/10.3390/e28010131 - 22 Jan 2026
Abstract
In this paper, we first prove (Theorem 1) that any two inputs producing the same output in a symmetric pair of discrete skew tent maps always have the same parity, meaning that they are either both even or both odd. Building on this [...] Read more.
In this paper, we first prove (Theorem 1) that any two inputs producing the same output in a symmetric pair of discrete skew tent maps always have the same parity, meaning that they are either both even or both odd. Building on this property, we then propose (Definition 1) a new discrete chaotic map and prove that (Theorem 2) the proposed map is a bijection for all control parameters. We further prove that (Theorem 3) the discrete Lyapunov exponent (dLE) of the proposed map is not only positive but also approaches the maximum value among all permutation maps over the integers {0,1,,2m1} as m gets larger. In other words, (Corollary 1) the proposed map asymptotically achieves the highest possible chaotic divergence among the permutation maps over the integers {0,1,,2m1}. To provide some further evidence that the proposed map is highly chaotic, we present at the end some results from the numerical experiments. We calculate the approximation and permutation entropy of the output integer sequences. We also show the NIST SP800-22 tests results and correlation properties of some derived binary sequences. Full article
(This article belongs to the Special Issue Discrete Math in Coding Theory, 2nd Edition)
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21 pages, 13708 KB  
Article
Image Encryption Using Chaotic Box Partition–Permutation and Modular Diffusion with PBKDF2 Key Derivation
by Javier Alberto Vargas Valencia, Mauricio A. Londoño-Arboleda, Hernán David Salinas Jiménez, Carlos Alberto Marín Arango and Luis Fernando Duque Gómez
J. Cybersecur. Priv. 2026, 6(1), 21; https://doi.org/10.3390/jcp6010021 - 22 Jan 2026
Abstract
This work presents a hybrid chaotic–cryptographic image encryption method that integrates a physical two-dimensional delta-kicked oscillator with a PBKDF2-HMAC-SHA256 key derivation function (KDF). The user-provided key material—a 12-character, human-readable key and four salt words—is transformed by the KDF into 256 bits of high-entropy [...] Read more.
This work presents a hybrid chaotic–cryptographic image encryption method that integrates a physical two-dimensional delta-kicked oscillator with a PBKDF2-HMAC-SHA256 key derivation function (KDF). The user-provided key material—a 12-character, human-readable key and four salt words—is transformed by the KDF into 256 bits of high-entropy data, which is then converted into 96 balanced decimal digits to seed the chaotic system. Encryption operates in the real number domain through a chaotic partition–permutation stage followed by modular diffusion. Experimental results confirm perfect reversibility, high randomness (Shannon entropy 7.9981), and negligible adjacent-pixel correlation. The method resists known- and chosen-plaintext attacks, showing no statistical dependence between plain and cipher images. Differential analysis yields NPCR99.6% and UACI33.9%, demonstrating complete diffusion. The PBKDF2-based key derivation expands the effective key space to 2256, eliminates weak-key conditions, and ensures full reproducibility. The proposed approach bridges deterministic chaos and modern cryptography, offering a secure, verifiable framework for protecting sensitive images. Full article
(This article belongs to the Section Cryptography and Cryptology)
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13 pages, 3108 KB  
Article
Analysis of Intestinal Microbiota Differences and Functional Prediction Between Sichuan-Tibetan Black Pigs and Landrace Pigs
by Lichun Jiang, Yi Qing, Kaiyuan Huang, Huiling Huang, Chengmin Li and Yanci Li
Microorganisms 2026, 14(1), 258; https://doi.org/10.3390/microorganisms14010258 - 22 Jan 2026
Abstract
This study aimed to investigate the structural differences and functional potential of the gut microbiota between Sichuan-Tibetan black pigs (n = 5) and Landrace pigs (n = 5) under identical rearing conditions. Fecal samples were collected and subjected to 16S rRNA [...] Read more.
This study aimed to investigate the structural differences and functional potential of the gut microbiota between Sichuan-Tibetan black pigs (n = 5) and Landrace pigs (n = 5) under identical rearing conditions. Fecal samples were collected and subjected to 16S rRNA gene sequencing followed by comprehensive bioinformatics analysis. The results revealed 963 and 910 operational taxonomic units (OTUs) in Sichuan-Tibetan black pigs and Landrace pigs, respectively, with 808 OTUs shared between the two breeds. While both breeds shared Firmicutes, Bacteroidota, and Proteobacteria as the dominant phyla, significant compositional differences were observed at the genus level. Sichuan-Tibetan black pigs exhibited higher abundance of Escherichia-Shigella, Streptococcus, Prevotella, Parabacteroides, and Collinsella, whereas Landrace pigs were enriched in Bacteroides. Alpha diversity analysis showed no significant differences in Shannon, Simpson, or ACE indices, though the Chao index differed markedly between the two groups. Beta diversity analysis (PCoA and NMDS) confirmed distinct microbial community structures between the breeds. Functional prediction analysis demonstrated that metabolic pathways dominated in both groups, but with notable functional differentiation: the microbiota of Sichuan-Tibetan black pigs showed significant enrichment in biosynthesis of secondary metabolites, microbial metabolism in diverse environments, and amino acid biosynthesis; whereas, Landrace pigs were characterized by enhanced carbon and energy metabolism pathways. Additionally, BugBase phenotype prediction revealed significant differences in stress tolerance, cell wall properties, and oxygen utilization capabilities between the two groups. These findings provide valuable insights into the breed-specific characteristics of gut microbiota in swine and establish a foundation for further research on host-microbe interactions and their implications for animal health and nutrition. Full article
(This article belongs to the Special Issue Gut Microbes and Probiotics)
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19 pages, 12627 KB  
Article
Radar-Based Insights into Seasonal Warm Cloud Dynamics in Northern Thailand: Properties, Kinematics and Occurrence
by Pakdee Chantraket and Parinya Intaracharoen
Atmosphere 2026, 17(1), 113; https://doi.org/10.3390/atmos17010113 - 21 Jan 2026
Viewed by 44
Abstract
This study presents a four-year (2021–2024) radar-based analysis of warm cloud (non-glaciated) dynamics across northern Thailand, specifically characterizing their properties, kinematics, and occurrence. Utilizing high-resolution S-band dual-polarization weather radar data, a total of 20,493 warm cloud events were tracked and analyzed, with identification [...] Read more.
This study presents a four-year (2021–2024) radar-based analysis of warm cloud (non-glaciated) dynamics across northern Thailand, specifically characterizing their properties, kinematics, and occurrence. Utilizing high-resolution S-band dual-polarization weather radar data, a total of 20,493 warm cloud events were tracked and analyzed, with identification based on a maximum reflectivity (≥35 dBZ) and a cloud top height below the seasonal 0 °C isotherm. Occurrence exhibited a profound seasonal disparity, with the rainy season (82.68% of events) dominating due to the influence of the moist Southwest Monsoon (SWM), while the spatial distribution confirmed that convective initiation is exclusively concentrated over mountainous terrain, underscoring orographic lifting as the essential mechanical trigger. Regarding properties, while vertical development and mass are greater in the warm seasons, microphysical intensity and Duration (mean ~26 min) remain highly uniform, suggesting a constrained, efficient warm rain process. In kinematics, clouds move fastest in winter (mean WSPD ~18.38 km/h), yet pervasive directional chaos (SD > 112°) highlights the strong influence of terrain-induced local circulations. In conclusion, while topography dictates where warm clouds form, the monsoon dictates when and how robustly they develop, creating intense, short-lived events that pose significant operational constraints for localized precipitation enhancement strategies. Full article
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17 pages, 3370 KB  
Article
Numerical Investigation of Dynamic Wrinkling Behaviors in Stiff-Film/PDMS-Substrate Structure
by Haohao Bi, Wenjie Li, Liuyun Wang and Bo Wang
Polymers 2026, 18(2), 292; https://doi.org/10.3390/polym18020292 - 21 Jan 2026
Viewed by 50
Abstract
Thin film/substrate structures based on the principle of buckling mechanics exhibit both excellent stretchability and mechanical stability, and they have been recognized as a critical configuration in the design of flexible electronic devices. During application, flexible electronic devices are usually subjected to complex [...] Read more.
Thin film/substrate structures based on the principle of buckling mechanics exhibit both excellent stretchability and mechanical stability, and they have been recognized as a critical configuration in the design of flexible electronic devices. During application, flexible electronic devices are usually subjected to complex dynamic environments. Therefore, it is of great significance to investigate the dynamic behavior of thin film/substrate structures for the design of flexible electronic devices. The bending energy, membrane energy, and kinetic energy of the thin film and the elastic energy of the substrate were calculated. On this basis, the dynamic equation of the thin film/substrate structure with a checkerboard wrinkled pattern was derived by applying the principle of minimum energy combined with the Lagrangian function. Numerical simulations were conducted on the system to analyze the effect of pre-strain and the Young’s modulus of substrate on the system’s potential energy function, simulate the temporal response of the system’s dynamic behavior, and investigate the influences of pre-strain and the Young’s modulus of substrate on system stability and the chaos critical value. Theoretical support is expected to be provided for the design of two-dimensional (2D) thin film/substrate structures through this research. Full article
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19 pages, 2477 KB  
Article
Effect of Hantavirus Infection on the Rodent Lung Microbiome: Specific Regulatory Roles of Host Species and Virus Types
by Yaru Xiong, Zhihui Dai, Fangling He, Rongjiao Liu, Juan Wang, Zhifei Zhan, Huayun Jia, Shengbao Chen and Liang Cai
Microorganisms 2026, 14(1), 244; https://doi.org/10.3390/microorganisms14010244 - 21 Jan 2026
Viewed by 48
Abstract
The lung-targeting characteristic of Hantavirus infection and the unclear mechanism underlying its interaction with the lung microbiome hampers the development of effective prevention and control strategies. In this study, lung tissues from Apodemus agrarius and Rattus norvegicus were collected at Hantavirus surveillance sites [...] Read more.
The lung-targeting characteristic of Hantavirus infection and the unclear mechanism underlying its interaction with the lung microbiome hampers the development of effective prevention and control strategies. In this study, lung tissues from Apodemus agrarius and Rattus norvegicus were collected at Hantavirus surveillance sites in Hunan Province. Metagenomic sequencing was subsequently applied to compare microbiome diversity, community structure, and function between infected and uninfected groups. Then the linear discriminant analysis effect size (LEfSe) was employed to identify key biomarkers. The results indicated that after infection with Hantaan virus (HTNV), Apodemus agrarius exhibited significantly increased evenness but markedly decreased richness of lung microbial communities, as reflected by consistent reductions in the number of observed species, Abundance-based Coverage Estimator (ACE) index, and Chao1 index. In contrast, Rattus norvegicus infected with Seoul virus (SEOV) showed no significant difference in microbial richness compared with uninfected controls, and even a slight increase was observed. These findings suggest that host species and virus type may play an important role in shaping microbial community responses. Furthermore, β-diversity analysis showed that the community structure was clearly separated by the host rodent species, as well as by their virus infection status. LEfSe analysis identified taxa with discriminatory power associated with infection status. Streptococcus agalactiae and Streptococcus were associated with SEOV-infected Rattus norvegicus, while Chlamydia and Chlamydia abortus were relatively enriched in uninfected Apodemus agrarius. This exploratory study reveals preliminary association between specific host—Hantavirus pairings (HTNV—Apodemus agrarius and SEOV—Rattus norvegicus) and the rodent lung microbiome, offering potential insights for future research into viral pathogenesis. Full article
(This article belongs to the Section Public Health Microbiology)
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32 pages, 18470 KB  
Article
Enhancing Neuromorphic Robustness via Recurrence Resonance: The Role of Shared Weak Attractors in Quantum Logic Networks
by Yu Huang and Yukio-Pegio Gunji
Biomimetics 2026, 11(1), 81; https://doi.org/10.3390/biomimetics11010081 - 19 Jan 2026
Viewed by 210
Abstract
Recurrence resonance, a phenomenon that enhances system computational capability by exploiting noise to amplify hidden attractors, holds significant potential for applications such as edge computing and neuromorphic computing. Although previous studies have extensively explored its characteristics, the underlying mechanism regarding its generation remains [...] Read more.
Recurrence resonance, a phenomenon that enhances system computational capability by exploiting noise to amplify hidden attractors, holds significant potential for applications such as edge computing and neuromorphic computing. Although previous studies have extensively explored its characteristics, the underlying mechanism regarding its generation remains unclear. Here, we employed a Stochastic Recurrent Neural Network to simulate neural networks under various coupling conditions. By introducing appropriate inhibitory connections and examining the state transition matrices, we analyzed the characteristics and correlations of attractor landscapes in both global and local systems to elucidate the generative mechanism behind the “Edge of Chaos” dynamics observed under the quantum logic connectivity structure during recurrence resonance. The results show that the strategic introduction of inhibitory connections enriches the system’s attractor landscape without compromising the intensity of recurrence resonance. Furthermore, we find that when neurons are coupled via quantum logic and noise intensity meets specific conditions, the strong attractors of the global system decompose into those of distinct local subsystems, accompanied by the sharing of structurally similar weak attractors. These findings suggest that under quantum logic connectivity, the interaction between the strong attractors of different subsystems is mediated by a background of shared weak attractors, thereby enhancing both the system’s robustness against noise and the diversity of its state evolution. Full article
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22 pages, 2600 KB  
Article
Risk Identification and Chaotic Synchronization Control for Spent Fuel Road Transportation Based on Complex Network Evolution Models
by Wen Chen, Shuliang Zou, Changjun Qiu and Meiyan Gan
Appl. Sci. 2026, 16(2), 994; https://doi.org/10.3390/app16020994 - 19 Jan 2026
Viewed by 64
Abstract
To improve the safety of road transportation of Spent Nuclear Fuel (SNF), this paper proposes a novel approach for risk identification and chaotic synchronous control in SNF road transportation systems. Firstly, a dynamic risk evolution model for the road transportation of SNF is [...] Read more.
To improve the safety of road transportation of Spent Nuclear Fuel (SNF), this paper proposes a novel approach for risk identification and chaotic synchronous control in SNF road transportation systems. Firstly, a dynamic risk evolution model for the road transportation of SNF is developed by analyzing the nonlinear interactions among vehicles, environmental conditions, and human factors using complex network analysis and nonlinear dynamics. Secondly, an enhanced K-shell decomposition method is applied to identify key risk nodes and assess the relative importance of different risk factors, providing a basis for targeted risk control. Finally, a chaotic synchronization control strategy based on Lyapunov stability is proposed to suppress risk divergence and restore system stability. Three targeted control schemes are evaluated by varying the control gain coefficients across the ‘Vehicle–Environment–Human’ dimensions. Simulation results indicate that the strategy prioritizing environmental and human risk control yields the fastest convergence, significantly outperforming vehicle-centric approaches. The results show that prioritizing both environmental and human-factor control is most effective for suppressing chaotic divergence. This provides a solid quantitative basis for the strategic shift from passive defense to active environmental warning, thereby significantly optimizing the dynamic risk management of the SNF transportation system. Full article
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25 pages, 5632 KB  
Article
Chaos-Enhanced, Optimization-Based Interpretable Classification Model and Performance Evaluation in Food Drying
by Cagri Kaymak, Bilal Alatas, Suna Yildirim, Ebru Akpinar, Gizem Gul Katircioglu, Murat Catalkaya, Orhan E. Akay and Mehmet Das
Biomimetics 2026, 11(1), 78; https://doi.org/10.3390/biomimetics11010078 - 18 Jan 2026
Viewed by 127
Abstract
Food drying is a widely used preservation technique; however, achieving high energy efficiency while maintaining product quality remains a significant challenge. This study aims to analyze comprehensive experimental data obtained during the hot-air drying process of the Paşa pear (regional pear) and the [...] Read more.
Food drying is a widely used preservation technique; however, achieving high energy efficiency while maintaining product quality remains a significant challenge. This study aims to analyze comprehensive experimental data obtained during the hot-air drying process of the Paşa pear (regional pear) and the system’s autonomous control structure using an explainable artificial intelligence (XAI)-based method. The intelligent drying system, operating for approximately 17.5 h under two temperatures (50 °C and 65 °C) and two air speeds (0.63 m/s and 1.03 m/s), continuously adjusted the temperature and air speed using a PLC-based control mechanism; it ensured stable control throughout the process by monitoring parameters such as product weight, moisture, inlet–outlet temperatures, and air speed in real time. Experimental results showed that drying performance varied significantly with operating conditions, with product mass decreasing from 450 g to 103 g. The innovative aspect of the study is that it obtained quantitative, interpretable rules without discretization by applying the oscillatory chaotic sunflower optimization algorithm (OCSFO) to multidimensional control and process data for the first time. Thanks to its chaotic search mechanism, OCSFO accurately analyzed complex drying dynamics and created rules that achieved over 90% success for high, medium, and low performance classes. The obtained explainable rules clearly demonstrate that drying temperature and air velocity are the dominant determining parameters for drying efficiency, while energy consumption and cabin temperature distribution play a supporting role in distinguishing between efficiency classes. These rules clearly demonstrate how changes in controlled temperature and air velocity, combined with product weight and heat transfer, affect drying performance. Thus, the study offers a robust framework that identifies critical factors affecting drying performance through a transparent artificial intelligence approach that leverages both the autonomous control system and XAI-based rule mining. Full article
(This article belongs to the Section Biological Optimisation and Management)
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20 pages, 377 KB  
Article
Modeling Service Experience and Sustainable Adoption of Drone Taxi Services in the UAE: A Behavioral Framework Informed by TAM and UTAUT
by Sami Miniaoui, Nasser A. Saif Almuraqab, Rashed Al Raees, Prashanth B. S. and Manoj Kumar M. V.
Sustainability 2026, 18(2), 922; https://doi.org/10.3390/su18020922 - 16 Jan 2026
Viewed by 127
Abstract
Urban air mobility solutions such as drone taxi services are increasingly viewed as a promising response to congestion, sustainability, and smart-city mobility challenges. However, the large-scale adoption of such services depends on users’ perceptions of service experience, trust, and readiness to engage with [...] Read more.
Urban air mobility solutions such as drone taxi services are increasingly viewed as a promising response to congestion, sustainability, and smart-city mobility challenges. However, the large-scale adoption of such services depends on users’ perceptions of service experience, trust, and readiness to engage with emerging technologies. This study investigates the determinants of sustainable adoption of drone taxi services in the United Arab Emirates (UAE) by examining technology readiness and service experience factors, interpreted through conceptual alignment with the Technology Acceptance Model (TAM) and the Unified Theory of Acceptance and Use of Technology (UTAUT). A structured questionnaire was administered to potential users, capturing perceptions related to optimism, innovation readiness, efficiency, control, privacy, insecurity, discomfort, inefficiency, and perceived operational risk, along with behavioral intention to adopt drone taxi services. Measurement reliability and validity were rigorously assessed using Cronbach’s alpha, composite reliability, average variance extracted (AVE), and the heterotrait–monotrait (HTMT) criterion. The validated latent construct scores were subsequently used to estimate a structural regression model examining the relative influence of each factor on adoption intention. The results indicate that privacy assurance and perceived control exert the strongest influence on behavioral intention, followed by optimism and innovation readiness, while negative readiness factors such as discomfort, insecurity, inefficiency, and perceived chaos demonstrate negligible effects. These findings suggest that in technologically progressive contexts such as the UAE, adoption intentions are primarily shaped by trust-building and empowerment-oriented perceptions rather than deterrence-based concerns. By positioning technology readiness and service experience constructs within established TAM and UTAUT theoretical perspectives, this study contributes a context-sensitive understanding of adoption drivers for emerging urban air mobility services. The findings offer practical insights for policy makers and service providers seeking to design user-centric, trustworthy, and sustainable drone taxi systems. Full article
(This article belongs to the Special Issue Service Experience and Servicescape in Sustainable Consumption)
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31 pages, 1726 KB  
Article
Entrepreneurship and Conway’s Game of Life: A Theoretical Approach from a Systemic Perspective
by Félix Oscar Socorro Márquez, Giovanni Efrain Reyes Ortiz and Harold Torrez Meruvia
Adm. Sci. 2026, 16(1), 45; https://doi.org/10.3390/admsci16010045 - 16 Jan 2026
Viewed by 218
Abstract
This study establishes a comprehensive structural isomorphism between Conway’s Game of Life and the entrepreneurial process, analysing the latter as a complex adaptive system governed by non-linear dynamics rather than linear predictability. Through a rigorous qualitative approach based on a systematic literature review [...] Read more.
This study establishes a comprehensive structural isomorphism between Conway’s Game of Life and the entrepreneurial process, analysing the latter as a complex adaptive system governed by non-linear dynamics rather than linear predictability. Through a rigorous qualitative approach based on a systematic literature review and abductive inference, the research identifies and correlates four fundamental dimensions: uncertainty, adaptability, growth, and sustainability. Transcending traditional metaphorical comparisons, this paper introduces a novel mathematical model that modifies Conway’s deterministic logic by incorporating an «Agency» variable (A). This critical addition quantifies how an entrepreneur’s internal capabilities can counterbalance environmental pressures (neighbourhood density) to determine survival thresholds, effectively transforming the simulation into a «Game of Life with Agency» where participants actively influence their viability potential (Ψ). The analysis explicitly correlates specific algorithmic configurations with real-world business phenomena: high-entropy initial states («The Soup») mirror early-stage market uncertainty where outcomes are probabilistic; «gliders» represent the necessity of strategic pivoting and continuous displacement for survival; and «oscillators» symbolise dynamic sustainability through rhythmic equilibrium rather than static permanence. Furthermore, the study validates the «Gosper Glider Gun» pattern as a model for scalable, generative growth. By bridging abstract systems theory with managerial practice, the research positions these simulations as «mental laboratories» for decision-making. The findings theoretically validate iterative methodologies like the Lean Startup and conclude that successful entrepreneurship operates on the «Edge of Chaos», providing a rigorous framework for navigating high stochastic uncertainty. Full article
(This article belongs to the Section International Entrepreneurship)
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17 pages, 7284 KB  
Article
Dynamics and Solution Behavior of the Variable-Order Fractional Newton–Leipnik System
by Rania Saadeh, Nidal E. Taha, Mohamed Hafez, Ghozail Sh. Al-Mutairi and Manahil A. M. Ashmaig
Mathematics 2026, 14(2), 312; https://doi.org/10.3390/math14020312 - 16 Jan 2026
Viewed by 183
Abstract
This paper considers the solution behavior and dynamical properties of the variable-order fractional Newton–Leipnik system defined via Liouville–Caputo derivatives of variable order. In contrast to integer-order models, the presence of variable-order fractional operators in the Newton–Leipnik structure enriches the model by providing memory-dependent [...] Read more.
This paper considers the solution behavior and dynamical properties of the variable-order fractional Newton–Leipnik system defined via Liouville–Caputo derivatives of variable order. In contrast to integer-order models, the presence of variable-order fractional operators in the Newton–Leipnik structure enriches the model by providing memory-dependent effects that vary with time; hence, it is capable of a broader and more flexible range of nonlinear responses. Numerical simulations have been conducted to study how different order functions influence the trajectory and qualitative dynamics: clear transitions in oscillatory patterns have been identified by phase portraits, time-series profiles, and three-dimensional state evolution. The work goes further by considering the development of bifurcations and chaotic regimes and stability shifts and confirms the occurrence of several phenomena unattainable in fixed-order and/or integer-order formulations. Analysis of Lyapunov exponents confirms strong sensitivity to the initial conditions and further details how the memory effects either reinforce or prevent chaotic oscillations according to the type of order function. The results, in fact, show that the variable-order fractional Newton–Leipnik framework allows for more expressive and realistic modeling of complex nonlinear phenomena and points out the crucial role played by evolving memory in controlling how the system moves between periodic, quasi-periodic, and chaotic states. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
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18 pages, 604 KB  
Article
Making Chaos Out of COVID-19 Testing
by Bo Deng, Jorge Duarte, Cristina Januário and Chayu Yang
Mathematics 2026, 14(2), 306; https://doi.org/10.3390/math14020306 - 15 Jan 2026
Viewed by 107
Abstract
Mathematical models for infectious diseases, particularly autonomous ODE models, are generally known to possess simple dynamics, often converging to stable disease-free or endemic equilibria. This paper investigates the dynamic consequences of a crucial, yet often overlooked, component of pandemic response: the saturation of [...] Read more.
Mathematical models for infectious diseases, particularly autonomous ODE models, are generally known to possess simple dynamics, often converging to stable disease-free or endemic equilibria. This paper investigates the dynamic consequences of a crucial, yet often overlooked, component of pandemic response: the saturation of public health testing. We extend the standard SIR model to include compartments for ‘Confirmed’ (C) and ‘Monitored’ (M) individuals, resulting in a new SICMR model. By fitting the model to U.S. COVID-19 pandemic data (specifically the Omicron wave of late 2021), we demonstrate that capacity constraints in testing destabilize the testing-free endemic equilibrium (E1). This equilibrium becomes an unstable saddle-focus. The instability is driven by a sociological feedback loop, where the rise in confirmed cases drive testing effort, modeled by a nonlinear Holling Type II functional response. We explicitly verify that the eigenvalues for the best-fit model satisfy the Shilnikov condition (λu>λs), demonstrating the system possesses the necessary ingredients for complex, chaotic-like dynamics. Furthermore, we employ Stochastic Differential Equations (SDEs) to show that intrinsic noise interacts with this instability to generate ’noise-induced bursting,’ replicating the complex wave-like patterns observed in empirical data. Our results suggest that public health interventions, such as testing, are not merely passive controls but active dynamical variables that can fundamentally alter the qualitative stability of an epidemic. Full article
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