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Keywords = periodic conditions

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19 pages, 28819 KiB  
Article
Dynamical Analysis, Feedback Control Circuit Implementation, and Fixed-Time Sliding Mode Synchronization of a Novel 4D Chaotic System
by Huaigu Tian, Xifeng Yi, Yang Zhang, Zhen Wang, Xiaojian Xi and Jindong Liu
Symmetry 2025, 17(8), 1252; https://doi.org/10.3390/sym17081252 (registering DOI) - 6 Aug 2025
Abstract
This paper presents a novel four-dimensional (4D) chaotic system exhibiting parametric symmetry breaking and multistability. Through equilibrium stability analysis, attractor reconstruction, Lyapunov Exponent spectra (LEs), and bifurcation diagrams, we reveal a continuous transition from symmetric period attractors to asymmetric chaotic states and rich [...] Read more.
This paper presents a novel four-dimensional (4D) chaotic system exhibiting parametric symmetry breaking and multistability. Through equilibrium stability analysis, attractor reconstruction, Lyapunov Exponent spectra (LEs), and bifurcation diagrams, we reveal a continuous transition from symmetric period attractors to asymmetric chaotic states and rich dynamical behaviors. Additionally, considering the potential of this system in practical applications, a feedback control simulation circuit is designed and implemented to ensure its stability and effectiveness under real-world conditions. Finally, among various control strategies, this paper proposes an innovative Fixed-Time Sliding Mode Synchronization (FTSMS) strategy, determines its synchronization convergence time, and provides an important theoretical foundation for the practical application of the system. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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13 pages, 1134 KiB  
Article
Biological and Physico-Chemical Properties of Lobosphaera sp. Packed in Metallized Polyethylene Terephthalate/Polyethylene (PETmet/PE)
by Valter F. R. Martins, Ana J. Alves, Fátima Poças, Manuela Pintado, Rui M. S. C. Morais and Alcina M. M. B. Morais
Phycology 2025, 5(3), 35; https://doi.org/10.3390/phycology5030035 (registering DOI) - 6 Aug 2025
Abstract
This study evaluated the effects of different storage conditions, varying in light exposure, relative humidity (RH), and packaging materials, on the physicochemical stability of Lobosphaera sp. biomass, the retention of bioactive compounds, and the bioactivity of its extracts. Under light and 75% RH, [...] Read more.
This study evaluated the effects of different storage conditions, varying in light exposure, relative humidity (RH), and packaging materials, on the physicochemical stability of Lobosphaera sp. biomass, the retention of bioactive compounds, and the bioactivity of its extracts. Under light and 75% RH, the biomass absorbed moisture over time, reaching 0.779 ± 0.003 g/g dry weight (DW) after three months. This was accompanied by a decline in luminosity, chroma, and hue values. In contrast, samples stored under other conditions showed minimal changes, indicating that high humidity, combined with light exposure, compromises biomass stability. Packaging in metalized polyethylene terephthalate (PETmet/PE) effectively preserved the water content, color, and carotenoid levels during a two-month storage period. Bioactive compounds extracted via hydroethanolic ultrasound-assisted extraction yielded 15.48 ± 1.35% DW. Total phenolic content (TPC) of the extracts declined over time in both PETmet/PE and low-density polyethylene (LDPE) packaging, though the decrease was less pronounced in PETmet/PE. Antioxidant activity, assessed via the ABTS assay, remained stable, regardless of storage duration or packaging. Antimicrobial activity of the extract decreased over time but remained more effective against Gram-positive bacteria (Staphylococcus aureus, Bacillus cereus, and Listeria monocytogenes), with PETmet/PE packaging better preserving antimicrobial efficacy than LDPE. These findings underscore the importance of optimized storage conditions and packaging for maintaining the quality and bioactivity of Lobosphaera sp. biomass and its extracts. Full article
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15 pages, 2417 KiB  
Article
Mechanical Behavior of Sustainable Concrete with Alkali-Activated Pumice as Cement Replacement for Walkway Slabs in Humid Tropical Climates
by Oscar Moreno-Vázquez, Pablo Julián López-González, Sergio Aurelio Zamora-Castro, Brenda Suemy Trujillo-García and Joaquín Sangabriel-Lomelí
Eng 2025, 6(8), 191; https://doi.org/10.3390/eng6080191 (registering DOI) - 6 Aug 2025
Abstract
Portland cement production is a major source of global CO2 emissions due to its high energy consumption and calcination processes. This study proposes a sustainable alternative through the partial replacement of cement with alkali-activated pumice, a naturally occurring aluminosilicate material with high [...] Read more.
Portland cement production is a major source of global CO2 emissions due to its high energy consumption and calcination processes. This study proposes a sustainable alternative through the partial replacement of cement with alkali-activated pumice, a naturally occurring aluminosilicate material with high regional availability. Mixes with 0%, 10%, 20%, and 30% cement replacement were designed for pedestrian slabs exposed to humid tropical conditions. Compressive strength was evaluated using non-destructive testing over a period of 364 days, and carbonation was analyzed at different ages. The results show that mixes with up to 30% pumice maintain adequate strength levels for light-duty applications, although with a more gradual strength development. A significant reduction in carbonation depth was also observed, especially in the mix with the highest replacement level, suggesting greater durability in aggressive environments. These findings support the use of pumice as a viable and sustainable supplementary cementitious material in tropical regions, promoting low-impact construction practices. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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24 pages, 2863 KiB  
Article
An Integrated Bond Graph Methodology for Building Performance Simulation
by Abdelatif Merabtine
Energies 2025, 18(15), 4168; https://doi.org/10.3390/en18154168 (registering DOI) - 6 Aug 2025
Abstract
Building performance simulation is crucial for the design and optimization of sustainable buildings. However, the increasing complexity of building systems necessitates advanced modeling techniques capable of handling multi-domain interactions. This paper presents a novel application of the bond graph (BG) methodology to simulate [...] Read more.
Building performance simulation is crucial for the design and optimization of sustainable buildings. However, the increasing complexity of building systems necessitates advanced modeling techniques capable of handling multi-domain interactions. This paper presents a novel application of the bond graph (BG) methodology to simulate and analyze the thermal behavior of an integrated trigeneration system within an experimental test cell. Unlike conventional simulation approaches, the BG framework enables unified modeling of thermal and hydraulic subsystems, offering a physically consistent and energy-based representation of system dynamics. The study investigates the system’s performance under both dynamic and steady-state conditions across two distinct climatic periods. Validation against experimental data reveals strong agreement between measured and simulated temperatures in heating and cooling scenarios, with minimal deviations. This confirms the method’s reliability and its capacity to capture transient thermal behaviors. The results also demonstrate the BG model’s effectiveness in supporting predictive control strategies, optimizing energy efficiency, and maintaining thermal comfort. By integrating hydraulic circuits and thermal exchange processes within a single modeling framework, this work highlights the potential of bond graphs as a robust and scalable tool for advanced building performance simulation. Full article
(This article belongs to the Section G: Energy and Buildings)
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20 pages, 6555 KiB  
Article
Statistical Study of Whistler-Mode Waves in the Magnetospheric Magnetic Ducts
by Salman A. Nejad and Anatoly V. Streltsov
Universe 2025, 11(8), 260; https://doi.org/10.3390/universe11080260 - 6 Aug 2025
Abstract
This paper presents a comprehensive statistical analysis of extremely/very low-frequency (ELF/VLF) whistler-mode waves observed within magnetic ducts (B-ducts) using data from NASA’s Magnetospheric Multiscale (MMS) mission. A total of 687 events were analyzed, comprising 504 occurrences on the dawn-side flank of [...] Read more.
This paper presents a comprehensive statistical analysis of extremely/very low-frequency (ELF/VLF) whistler-mode waves observed within magnetic ducts (B-ducts) using data from NASA’s Magnetospheric Multiscale (MMS) mission. A total of 687 events were analyzed, comprising 504 occurrences on the dawn-side flank of the magnetosphere and 183 in the nightside magnetotail, to investigate the spatial distribution and underlying mechanisms of wave–particle interactions. We identify distinct differences between these regions by examining key parameters such as event width, frequency, plasma density, and magnetic field extrema within B-ducts. Using an independent two-sample t-test, we assess the statistical significance of variations in these parameters between different observation periods. This study provides valuable insights into the magnetospheric conditions influencing B-duct formation and wave propagation, offering a framework for understanding ELF/VLF wave dynamics in Earth’s space environment. Full article
(This article belongs to the Section Space Science)
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19 pages, 451 KiB  
Article
Examining the Structure of Directed Motivational Currents (DMCs) Among Secondary and Tertiary English as a Second Language Learners
by Chuanwei Huo, Lawrence Jun Zhang and Jason M. Stephens
Behav. Sci. 2025, 15(8), 1066; https://doi.org/10.3390/bs15081066 - 6 Aug 2025
Abstract
Motivation remains a central concern in second language (L2) and English as a foreign language (EFL) education, yet its underlying mechanisms are insufficiently understood. This study employs the theory of Directed Motivational Currents (DMCs) to explore periods of intense, sustained L2 motivation among [...] Read more.
Motivation remains a central concern in second language (L2) and English as a foreign language (EFL) education, yet its underlying mechanisms are insufficiently understood. This study employs the theory of Directed Motivational Currents (DMCs) to explore periods of intense, sustained L2 motivation among Chinese adolescent EFL learners across secondary and tertiary levels. Through in-depth interviews with ten participants, this research identified the conditions (e.g., collaborative peer dynamics, vivid goal visualization) that triggered their DMC experiences. The data also highlighted how facilitative elements—such as clear starting points, personalized goal alignment, behavioral routines, and timely feedback—played a crucial role in initiating and sustaining these motivational currents. These findings contribute to DMC theory by revealing how intrinsic and extrinsic factors jointly foster and maintain high levels of motivation over time, offering valuable insights for designing targeted interventions to enhance EFL motivation and learning among Chinese adolescents. Full article
(This article belongs to the Section Educational Psychology)
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18 pages, 732 KiB  
Article
L-Arginine Effect as an Additive on Overall Performance, Health Status, and Expression of Stress Molecular Markers in Nile Tilapia (Oreochromis niloticus) Under Chronic Salinity Exposure
by Andrea Itzel Munguía-Casillas, María Teresa Viana, Miroslava Vivanco-Aranda, Luis Eduardo Ruiz-González, Emyr Saul Peña-Marín and Oscar Basilio Del Rio-Zaragoza
Fishes 2025, 10(8), 387; https://doi.org/10.3390/fishes10080387 - 6 Aug 2025
Abstract
Growing freshwater fish in saline environments is being explored as a potential solution to the freshwater shortage. However, growing these organisms in suboptimal salinity conditions leads to chronic stress that can be challenging to manage. To address this goal, it is crucial to [...] Read more.
Growing freshwater fish in saline environments is being explored as a potential solution to the freshwater shortage. However, growing these organisms in suboptimal salinity conditions leads to chronic stress that can be challenging to manage. To address this goal, it is crucial to improve the health of fish through the use of dietary supplements. This study evaluated the effects of varying levels of arginine supplementation on the growth, health status, and expression of stress-related molecular markers in juveniles of Nile tilapia exposed to chronic salinity stress. The tilapia were fed four experimental diets supplemented with 0, 1, 2, and 3% of L-arginine (T0, T1, T2, and T3). After an acclimatization period, the tilapias were exposed to a salinity level of 20‰ for 57 days in a recirculating aquaculture system. Our findings revealed that overall performance parameters were significantly influenced by L-arginine supplementation, except for the condition factor, viscerosomatic index, and hepatosomatic index. Additionally, intermediate levels of L-arginine supplementation positively influenced various blood parameters, including hematological profiles (hemoglobin and leukocytes), blood chemistry (total protein, albumin, globulin, and triglycerides), and the frequency of certain nuclear abnormalities. Furthermore, L-arginine supplementation appeared to regulate the expression of molecular markers related to stress and the immune system. In conclusion, this study indicates that L-arginine supplementation can help alleviate the chronic stress caused by salinity in juvenile Nile tilapia. Full article
(This article belongs to the Special Issue Fish Hematology)
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18 pages, 4216 KiB  
Article
Screening and Application of Highly Efficient Rhizobia for Leguminous Green Manure Astragalus sinicus in Lyophilized Inoculants and Seed Coating
by Ding-Yuan Xue, Wen-Feng Chen, Guo-Ping Yang, You-Guo Li and Jun-Jie Zhang
Plants 2025, 14(15), 2431; https://doi.org/10.3390/plants14152431 - 6 Aug 2025
Abstract
Astragalus sinicus, a key leguminous green manure widely cultivated in Southern China’s rice-based cropping systems, plays a pivotal role in sustainable agriculture by enhancing soil organic matter sequestration, improving rice yield, and elevating grain quality. The symbiotic nitrogen-fixing association between A. sinicus [...] Read more.
Astragalus sinicus, a key leguminous green manure widely cultivated in Southern China’s rice-based cropping systems, plays a pivotal role in sustainable agriculture by enhancing soil organic matter sequestration, improving rice yield, and elevating grain quality. The symbiotic nitrogen-fixing association between A. sinicus and its matching rhizobia is fundamental to its agronomic value; however, suboptimal inoculant efficiency and field application methodologies constrain its full potential. To address these limitations, we conducted a multi-phase study involving (1) rhizobial strain screening under controlled greenhouse conditions, (2) an optimized lyophilization protocol evaluating cryoprotectant (trehalose, skimmed milk powder and others), and (3) seed pelleting trails with rhizobial viability and nodulation assessments over different storage periods. Our results demonstrate that Mesorhizobium huakuii CCBAU 33470 exhibits a superior nitrogen-fixing efficacy, significantly enhancing key traits in A. sinicus, including leaf chlorophyll content, tiller number, and aboveground biomass. Lyophilized inoculants prepared with cryoprotectants (20% trehalose or 20% skimmed milk powder) maintained >90% bacterial viability for 60 days and markedly improved nodulation capacity relative to unprotected formulations. The optimized seed pellets sustained high rhizobial loads (5.5 × 103 cells/seed) with an undiminished viability after 15 days of storage and nodulation ability after 40 days of storage. This integrated approach of rhizobial selection, inoculant formulation, and seed coating overcomes cultivation bottlenecks, boosting symbiotic nitrogen fixation for A. sinicus cultivation. Full article
(This article belongs to the Topic New Challenges on Plant–Microbe Interactions)
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14 pages, 5479 KiB  
Article
Assessment of Three Provenances of Juglans neotropica Diels to Identify Optimal Seed Sources in the Northern Ecuadorian Andes
by Jorge-Luis Ramírez-López, Mario Añazco, Hugo Vallejos, Carlos Arcos and Kelly Estrada
Int. J. Plant Biol. 2025, 16(3), 87; https://doi.org/10.3390/ijpb16030087 (registering DOI) - 6 Aug 2025
Abstract
Identifying optimal seed sources is critical for the propagation and restoration of Juglans neotropica Diels in the northern Ecuadorian Andes, where populations are declining due to habitat loss and overexploitation. This study evaluated the seed quality and germination performance of Juglans neotropica from [...] Read more.
Identifying optimal seed sources is critical for the propagation and restoration of Juglans neotropica Diels in the northern Ecuadorian Andes, where populations are declining due to habitat loss and overexploitation. This study evaluated the seed quality and germination performance of Juglans neotropica from three ecologically distinct provenances: a natural regeneration site (Cuyuja), a pure plantation (Natabuela), and an agroforestry system (Pimampiro). Five phenotypically superior trees were selected from each site, and germination was assessed under controlled nursery conditions over a 150-day period using a completely randomized design. Initial viability tests confirmed the physiological integrity of the seeds across all provenances. Germination onset ranged from day 55 to day 73, with significant differences in germination percentage, speed, and uniformity. The agroforestry provenance showed the highest germination rate (69%) and superior performance in all physiological indices, while natural regeneration had the lowest (15%). Post-trial viability assessments indicated that a substantial proportion of non-germinated seeds from Cuyuja remained dormant or deteriorated. These findings underscore the role of agroforestry systems in enhancing seed physiological quality and support their prioritization for large-scale propagation and ecological restoration initiatives involving Juglans neotropica. Full article
(This article belongs to the Section Plant Reproduction)
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17 pages, 1323 KiB  
Article
The Effect of Nitrogen Fertilizer Placement and Timing on Winter Wheat Grain Yield and Protein Concentration
by Brent Ballagh, Anna Ballagh, Jacob Bushong and Daryl Brian Arnall
Agronomy 2025, 15(8), 1890; https://doi.org/10.3390/agronomy15081890 - 5 Aug 2025
Abstract
Nitrogen (N) fertilizer management in winter wheat production faces challenges from volatilization losses and sub-optimal application strategies. This is particularly problematic in the Southern Great Plains, where environmental conditions during top-dressing periods favor N losses. This study evaluated the effects of a fertilizer [...] Read more.
Nitrogen (N) fertilizer management in winter wheat production faces challenges from volatilization losses and sub-optimal application strategies. This is particularly problematic in the Southern Great Plains, where environmental conditions during top-dressing periods favor N losses. This study evaluated the effects of a fertilizer placement method, enhanced-efficiency fertilizers, and application timing on grain yield and protein concentration (GPC) across six site-years in Oklahoma (2016–2018). Treatments included broadcast applications of untreated urea and SuperU® (urease/nitrification inhibitor-treated urea). These were compared with subsurface placement using single-disc and double-disc drilling systems, applied at 67 kg N ha−1 during January, February, or March. Subsurface placement increased the grain yield by 324–391 kg ha−1 compared to broadcast applications at sites with favorable soil conditions. However, responses varied significantly across environments. Enhanced-efficiency fertilizers showed limited advantages over untreated urea. Benefits were most pronounced during February applications under conditions favoring volatilization losses. Application timing effects were more consistent for GPC than for the yield. Later applications (February–March) increased GPC by 0.8–1.2% compared to January applications. Treatment efficacy was strongly influenced by soil pH, equipment performance, and post-application environmental conditions. This indicates that N management benefits are highly site-specific. These findings demonstrate that subsurface placement can improve nitrogen use efficiency (NUE) under appropriate conditions. However, success depends on matching application strategies to local soil and environmental factors rather than adopting universal recommendations. Full article
(This article belongs to the Special Issue Fertility Management for Higher Crop Productivity)
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19 pages, 15989 KiB  
Article
Influence of Radial Pressure Gradient on Secondary Flows: Numerical Study and Design Optimization for High-Speed Annular Sector Cascades
by Moritz Klappenberger, Christian Landfester, Robert Krewinkel and Martin Böhle
Int. J. Turbomach. Propuls. Power 2025, 10(3), 18; https://doi.org/10.3390/ijtpp10030018 - 5 Aug 2025
Abstract
Secondary flow phenomena have a significant influence on the generation of losses and the propagation of coolant on the turbine end walls. The majority of film cooling studies are carried out on linear rather than annular cascades due to the structural simplicity and [...] Read more.
Secondary flow phenomena have a significant influence on the generation of losses and the propagation of coolant on the turbine end walls. The majority of film cooling studies are carried out on linear rather than annular cascades due to the structural simplicity and ease of measurement integration of the former. This approach neglects the effects of the radial pressure gradient that is naturally imposed on the vortex flow in annular cascades. The first part of this paper numerically investigates the effect of the radial pressure gradient on the secondary flow under periodic flow conditions by comparing a linear and an annular case. It is shown that the radial pressure gradient has a significant influence on the propagation of the secondary flow induced vortices in the wake of the nozzle guide vanes (NGV). In the second part of the paper, a novel approach of a five-passage annular sector cascade is presented, which avoids the hub boundary layer separation, as is typical for this type of test rig. To increase the periodicity, a benchmark approach is introduced that includes multiple pointwise and integral flow quantities at different axial positions. Based on the optimized best-case design, general design guidelines are derived that allow a straightforward design process for annular sector cascades. Full article
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25 pages, 13175 KiB  
Article
Fault Diagnosis for CNC Machine Tool Feed Systems Based on Enhanced Multi-Scale Feature Network
by Peng Zhang, Min Huang and Weiwei Sun
Lubricants 2025, 13(8), 350; https://doi.org/10.3390/lubricants13080350 - 5 Aug 2025
Abstract
Despite advances in Convolutional Neural Networks (CNNs) for intelligent fault diagnosis in CNC machine tools, bearing fault diagnosis in CNC feed systems remains challenging, particularly in multi-scale feature extraction and generalization across operating conditions. This study introduces an enhanced multi-scale feature network (MSFN) [...] Read more.
Despite advances in Convolutional Neural Networks (CNNs) for intelligent fault diagnosis in CNC machine tools, bearing fault diagnosis in CNC feed systems remains challenging, particularly in multi-scale feature extraction and generalization across operating conditions. This study introduces an enhanced multi-scale feature network (MSFN) that addresses these limitations through three integrated modules designed to extract critical fault features from vibration signals. First, a Soft-Scale Denoising (S2D) module forms the backbone of the MSFN, capturing multi-scale fault features from input signals. Second, a Multi-Scale Adaptive Feature Enhancement (MS-AFE) module based on long-range weighting mechanisms is developed to enhance the extraction of periodic fault features. Third, a Dynamic Sequence–Channel Attention (DSCA) module is incorporated to improve feature representation across channel and sequence dimensions. Experimental results on two datasets demonstrate that the proposed MSFN achieves high diagnostic accuracy and exhibits robust generalization across diverse operating conditions. Moreover, ablation studies validate the effectiveness and contributions of each module. Full article
(This article belongs to the Special Issue Advances in Tool Wear Monitoring 2025)
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15 pages, 750 KiB  
Review
Using Biocontrol Fungi to Control Helminthosis in Wild Animals: An Innovative Proposal for the Health and Conservation of Species
by Júlia dos Santos Fonseca, Beatriz Bacelar Barbosa, Adolfo Paz Silva, María Sol Arias Vázquez, Cristiana Filipa Cazapal Monteiro, Huarrisson Azevedo Santos and Jackson Victor de Araújo
Pathogens 2025, 14(8), 775; https://doi.org/10.3390/pathogens14080775 - 5 Aug 2025
Abstract
Helminth parasites of wild animals represent a major threat to the health of these animals, leading to significant losses in performance, health, and zoonotic implications. In some zoos, anthelmintics have traditionally been used to control these parasites, many of which are also zoonotic. [...] Read more.
Helminth parasites of wild animals represent a major threat to the health of these animals, leading to significant losses in performance, health, and zoonotic implications. In some zoos, anthelmintics have traditionally been used to control these parasites, many of which are also zoonotic. Other actions, such as the removal of organic waste, have also been adopted. Few or no control measures are applied to free-ranging wild animals. Helminthophagous fungi are a promising biological alternative. When animals ingest fungal spores, they are excreted in their feces, where they trap and destroy helminth larvae and eggs, preventing and reducing the parasite load in the environment. Another alternative is to administer fungi by spraying them directly into the environment. This review aims to examine the use of helminthophagous fungi in the control of helminthiases in wild animals, highlighting their potential to minimize dependence on chemical treatments and promote sustainable animal breeding and production. There are many challenges to making this viable, such as environmental variability, stability of formulations, and acceptance of this new technology. These fungi have been shown to reduce parasite burdens in wild animals by up to 75% and can be administered through the animals’ feeding troughs. To date, evidence shows that helminthophagous fungi can reliably curb environmental parasite loads for extended periods, offering a sustainable alternative to repeated anthelmintic dosing. Their use has been linked to tangible gains in body condition, weight, and overall welfare in various captive and free-ranging wildlife species. Full article
(This article belongs to the Section Parasitic Pathogens)
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34 pages, 2291 KiB  
Article
A Study of Periodicities in a One-Dimensional Piecewise Smooth Discontinuous Map
by Rajanikant A. Metri, Bhooshan Rajpathak, Kethavath Raghavendra Naik and Mohan Lal Kolhe
Mathematics 2025, 13(15), 2518; https://doi.org/10.3390/math13152518 - 5 Aug 2025
Abstract
In this study, we investigate the nonlinear dynamical behavior of a one-dimensional linear piecewise-smooth discontinuous (LPSD) map with a negative slope, motivated by its occurrence in systems exhibiting discontinuities, such as power electronic converters. The objective of the proposed research is to develop [...] Read more.
In this study, we investigate the nonlinear dynamical behavior of a one-dimensional linear piecewise-smooth discontinuous (LPSD) map with a negative slope, motivated by its occurrence in systems exhibiting discontinuities, such as power electronic converters. The objective of the proposed research is to develop an analytical approach. Analytical conditions are derived for the existence of stable period-1 and period-2 orbits within the third quadrant of the parameter space defined by slope coefficients a<0 and b<0. The coexistence of multiple attractors is demonstrated. We also show that a novel class of orbits exists in which both points lie entirely in either the left or right domain. These orbits are shown to eventually exhibit periodic behavior, and a closed-form expression is derived to compute the number of iterations required for a trajectory to converge to such orbits. This method also enhances the ease of analyzing system stability by mapping the state–variable dynamics using a non-smooth discontinuous map. The analytical findings are validated using bifurcation diagrams, cobweb plots, and basin of attraction visualizations. Full article
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25 pages, 4865 KiB  
Article
Mathematical Modeling, Bifurcation Theory, and Chaos in a Dusty Plasma System with Generalized (r, q) Distributions
by Beenish, Maria Samreen and Fehaid Salem Alshammari
Axioms 2025, 14(8), 610; https://doi.org/10.3390/axioms14080610 (registering DOI) - 5 Aug 2025
Abstract
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. [...] Read more.
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article
(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)
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