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Search Results (350)

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Keywords = attraction basins

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17 pages, 2298 KB  
Article
Pollution Characteristics of Typical Pesticides and Multi-Level Ecological Risk Assessment in the Jiujiang Port Basin
by Deming Gu, Yanli Mao, Xunhai Zhang, Miao Chen, Haoxiang Rong and Mingfei Yue
Water 2025, 17(20), 2964; https://doi.org/10.3390/w17202964 - 15 Oct 2025
Abstract
Pesticides have attracted widespread attention as significant factors affecting aquatic ecosystem diversity. Jiujiang Port, located at the confluence of the Yangtze River and Poyang Lake, is the largest hub port in Jiujiang City and also an important agricultural production area. However, the characteristics [...] Read more.
Pesticides have attracted widespread attention as significant factors affecting aquatic ecosystem diversity. Jiujiang Port, located at the confluence of the Yangtze River and Poyang Lake, is the largest hub port in Jiujiang City and also an important agricultural production area. However, the characteristics and ecological risks of pesticide pollution in this basin have rarely been reported. In this study, we investigated the contamination profiles of 49 typical pesticides in surface waters in the Jiujiang Port area and conducted a multi-level ecological risk assessment using the Risk Quotient (RQ) method, semi-probabilistic risk assessment (RQf), and Joint Probability Curve (JPC) approach. The results showed that the average concentrations of triazine, carbamate, neonicotinoid, and organophosphorus pesticides were 3.063 ng·L−1, 0.321 ng·L−1, 3.752 ng·L−1, and 1.554 ng·L−1, respectively. Among them, hexazinone was the most predominant contaminant, with an average concentration of 19.209 ng·L−1. Twenty pesticides were detected at frequencies exceeding 80%, and the overall pollution level was higher in the wet season than in the dry season. The RQ assessment indicated that 11 pesticides posed low or higher risks in either the wet or dry season, with imidacloprid, simazine, and terbutryn presenting moderate risks and hexazinone, chlorpyrifos, and diazinon posing high risks. The RQf values of hexazinone, chlorpyrifos, diazinon, imidacloprid, simazine, and terbutryn all exceeded 1 in both seasons, indicating substantial ecological risks to aquatic organisms in the Jiujiang Port basin. The JPC evaluation suggested that hexazinone may pose a moderate risk to 0.3–6% of aquatic species, while chlorpyrifos, imidacloprid, and terbutryn were associated with a low risk. This study elucidates the contamination characteristics, spatiotemporal distribution, and ecological risks of pesticides in surface water, providing a scientific basis for the protection of aquatic biodiversity and the management of pesticide pollution in the Jiujiang Port basin. Full article
(This article belongs to the Section Water Quality and Contamination)
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14 pages, 752 KB  
Article
Basins of Attraction for Third-Order Sigmoid Beverton Holt Difference Equation
by Mustafa R. S. Kulenović and Ryan Sullivan
Mathematics 2025, 13(18), 2990; https://doi.org/10.3390/math13182990 - 16 Sep 2025
Viewed by 292
Abstract
The third-order difference equation [...] Read more.
The third-order difference equation yn+1=a1yn21+yn2+a2yn121+yn12+a3yn221+yn22, as a potential discrete time model of population dynamics with three generation involved, is studied. The parts of the basins of attraction of three equilibrium points that this equation admits are described. Some results about period-two and period-three solutions have been established. Full article
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30 pages, 4102 KB  
Article
Integrating Species Richness, Distribution and Human Pressures to Assess Conservation Priorities in High Andean Salares
by Marcelo Hernández-Rojas, Rodrigo A. Estévez, Cristian Romero, Sebastián Pérez and Fabio A. Labra
Sustainability 2025, 17(18), 8139; https://doi.org/10.3390/su17188139 - 10 Sep 2025
Viewed by 503
Abstract
High Andean salares and their surrounding basins host unique ecosystems and rich biodiversity. Increasing global demand for lithium and brines in these environments have attracted significant international investment, raising both economic expectations and socio-environmental concerns. This poses major challenges for biodiversity conservation, governance [...] Read more.
High Andean salares and their surrounding basins host unique ecosystems and rich biodiversity. Increasing global demand for lithium and brines in these environments have attracted significant international investment, raising both economic expectations and socio-environmental concerns. This poses major challenges for biodiversity conservation, governance models, and the management of socio-environmental conflicts. One of the main challenges for effective conservation is the lack of systematic biodiversity inventories and an integrated conservation diagnosis. In this study, we leverage range–diversity plot analysis to describe the patterns of biological diversity and species distribution in High Andean salares. We then integrate this information with estimates of available suitable habitat area and degree of human pressure, to categorize the priorities for the salt flats. Our results show that many salt flats serve as biodiversity hotspots, dominated by species with wide distribution ranges. A significant number of salt flats host rare species, indicating the necessity for focused conservation initiatives. The studied salt flats warrant prioritisation for restoration, protection, and the enhancement of public policies and social awareness initiatives. Current conservation strategies should be consistent with the Network of Protected Salt Flats as outlined in the National Lithium Strategy, thereby enhancing socio-environmental governance in these delicate socio-ecosystems. Full article
(This article belongs to the Section Sustainability, Biodiversity and Conservation)
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26 pages, 1159 KB  
Article
On High-Value Mixed Cropping System: Four-Way Evolutionary Game Analysis of HMC Synergy of Circular and Sharing Economy for Multiple Low-to-Middle-Income Farmer Families
by Duc Nghia Vu, Truc Le Nguyen, Mai Huong Nguyen Thi, Gia Kuop Nguyen, Duc Binh Vo, Ngoc Anh Nguyen and Huy Duc Nguyen
Sustainability 2025, 17(17), 7611; https://doi.org/10.3390/su17177611 - 23 Aug 2025
Viewed by 784
Abstract
This paper introduces a novel four-party evolutionary game model to analyze cooperation dynamics in High-Value Mixed Cropping (HMC) systems integrating non-pesticide cacao, cashew nut, and free-range chicken farming within circular and sharing economy frameworks. The model uniquely examines strategic interactions among local government [...] Read more.
This paper introduces a novel four-party evolutionary game model to analyze cooperation dynamics in High-Value Mixed Cropping (HMC) systems integrating non-pesticide cacao, cashew nut, and free-range chicken farming within circular and sharing economy frameworks. The model uniquely examines strategic interactions among local government and three farming family types (cacao, cashew, and chicken), incorporating both regulatory mechanisms and cooperative behaviors. Through rigorous stability analysis and MATLAB simulations based on empirical data from Southeast Vietnam, we identify precise conditions for Evolutionarily Stable Strategies (ESSs) that sustain long-term cooperation. Our results demonstrate that government incentives (subsidies, technical support) and reputational sanctions critically shape farmers’ and consumers’ payoffs, thereby steering the system toward collective action equilibria. In particular, increasing the strength of positive incentives or reputational benefits enlarges the basin of attraction for full-cooperation ESSs, regardless of initial strategy distributions. Conversely, overly punitive sanctions can destabilize collaborative outcomes. These findings underscore the pivotal role of well-balanced policy instruments in fostering resilience, innovation, and resource circulation within rural agroecosystems. Finally, we propose targeted policy recommendations, such as graduated subsidy schemes, participatory monitoring platforms, and cooperative branding initiatives, to reinforce circular economy practices and accelerate progress toward the United Nations Sustainable Development Goals. Full article
(This article belongs to the Section Waste and Recycling)
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34 pages, 2291 KB  
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
Viewed by 675
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 KB  
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 - 5 Aug 2025
Cited by 1 | Viewed by 463
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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13 pages, 6786 KB  
Article
Hydropower Microgeneration in Detention Basins: A Case Study of Santa Lúcia Basin in Brazil
by Azuri Sofia Gally Koroll, Rodrigo Perdigão Gomes Bezerra, André Ferreira Rodrigues, Bruno Melo Brentan, Joaquín Izquierdo and Gustavo Meirelles
Water 2025, 17(15), 2219; https://doi.org/10.3390/w17152219 - 24 Jul 2025
Viewed by 829
Abstract
Flood control infrastructure is essential for the development of cities and the population’s well-being. The goal is to protect human and economic resources by reducing the inundation area and controlling the flood level and peak discharges. Detention basins can do this by storing [...] Read more.
Flood control infrastructure is essential for the development of cities and the population’s well-being. The goal is to protect human and economic resources by reducing the inundation area and controlling the flood level and peak discharges. Detention basins can do this by storing a large volume of water to be released after the peak discharge. By doing this, a large amount of energy is stored, which can be recovered via micro-hydropower. In addition, as the release flow is controlled and almost constant, Pumps as Turbines (PAT) could be a feasible and economic option in these cases. Thus, this study investigates the feasibility of micro-hydropower (MHP) in urban detention basins, using the Santa Lúcia detention basin in Belo Horizonte as a case study. The methodology involved hydrological modeling, hydraulic analysis, and economic and environmental assessment. The results demonstrated that PAT selection has a crucial role in the feasibility of the MHP, and exploiting rainfall with lower intensities but higher frequencies is more attractive. Using multiple PATs with different operating points also showed promising results in improving energy production. In addition to the economic benefits, the MHP in the detention basin produces minimal environmental impact and, as it exploits a wasted energy source, it also reduces the carbon footprint in the urban water cycle. Full article
(This article belongs to the Special Issue Research Status of Operation and Management of Hydropower Station)
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22 pages, 2652 KB  
Article
Niching-Driven Divide-and-Conquer Hill Exploration
by Junchen Wang, Changhe Li and Yiya Diao
Appl. Syst. Innov. 2025, 8(4), 101; https://doi.org/10.3390/asi8040101 - 22 Jul 2025
Viewed by 722
Abstract
Optimization problems often feature local optima with a significant difference in the basin of attraction (BoA), making evolutionary computation methods prone to discarding solutions located in less-attractive BoAs, thereby posing challenges to the search for optima in these BoAs. To enhance the ability [...] Read more.
Optimization problems often feature local optima with a significant difference in the basin of attraction (BoA), making evolutionary computation methods prone to discarding solutions located in less-attractive BoAs, thereby posing challenges to the search for optima in these BoAs. To enhance the ability to find these optima, various niching methods have been proposed to restrict the competition scope of individuals to their specific neighborhoods. However, redundant searches in more-attractive BoAs as well as necessary searches in less-attractive BoAs can only be promoted simultaneously by these methods. To address this issue, we propose a general framework for niching methods named niching-driven divide-and-conquer hill exploration (NDDCHE). Through gradually learning BoAs from the search results of a niching method and dividing the problem into subproblems with a much smaller number of optima, NDDCHE aims to bring a more balanced distribution of searches in the BoAs of optima found so far, and thus enhance the niching method’s ability to find optima in less-attractive BoAs. Through experiments where niching methods with different categories of niching techniques are integrated with NDDCHE and tested on problems with significant differences in the size of the BoA, the effectiveness and the generalization ability of NDDCHE are proven. Full article
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33 pages, 18807 KB  
Article
Recreational Fisheries Encountering Flagship Species: Current Conditions, Trend Forecasts and Recommendations
by Yixin Qian, Jingzhou Liu, Li Liu, Xueming Wang and Jianming Zheng
Fishes 2025, 10(7), 337; https://doi.org/10.3390/fishes10070337 - 9 Jul 2025
Viewed by 648
Abstract
Recreational fisheries increasingly intersect with the habitats of flagship species, i.e., species that attract public attention and drive conservation efforts, raising potential ecological conflicts. This study investigated the spatial coupling between recreational fisheries and three flagship species in the Yangtze River Basin: the [...] Read more.
Recreational fisheries increasingly intersect with the habitats of flagship species, i.e., species that attract public attention and drive conservation efforts, raising potential ecological conflicts. This study investigated the spatial coupling between recreational fisheries and three flagship species in the Yangtze River Basin: the Chinese alligator (Alligator sinensis), the Yangtze finless porpoise (Neophocaena phocaenoides), and the scaly-sided merganser (Mergus squamatus). Drawing on over 10,000 fishing Points of Interest recorded between 2015 and 2024 and over 300 verified species occurrences, this study applied a Random Forest model with spatial integration and a Maximum Entropy model to examine estimated current distributions and forecast interactions from 2025 to 2035. Flagship species habitat suitability was modeled and projected at a spatial resolution of 1 km, while recreational fishing density was resolved on a coarser grid of 1.875° × 1.25° in latitude–longitude dimensions. Results reveal a substantial increase in high-risk overlap zones. For example, high-density fishing areas within high-suitability habitats for the scaly-sided merganser expanded from 0 km2 in 2015 to 85,359 km2 in 2024. Projections indicate continued intensification of such overlaps, particularly in regions including Ma’anshan–Wuhu, the Taihu–Chaohu–Poyang lake system, and Yibin. These findings offer robust, model-driven evidence of growing spatial conflicts and offer actionable insights for ecosystem-based governance. The methodological framework is transferable and supports broader applications in other regions and species under ecological sustainability goals. Full article
(This article belongs to the Section Biology and Ecology)
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27 pages, 3553 KB  
Article
Mitigating Selection Bias in Local Optima: A Meta-Analysis of Niching Methods in Continuous Optimization
by Junchen Wang, Changhe Li and Yiya Diao
Information 2025, 16(7), 583; https://doi.org/10.3390/info16070583 - 7 Jul 2025
Cited by 1 | Viewed by 354
Abstract
As mainstream solvers for black-box optimization problems, evolutionary computation (EC) methods struggle with finding desired optima of lower attractiveness. Researchers have designed benchmark problems for simulating this scenario and proposed a large number of niching methods for solving those problems. However, factors causing [...] Read more.
As mainstream solvers for black-box optimization problems, evolutionary computation (EC) methods struggle with finding desired optima of lower attractiveness. Researchers have designed benchmark problems for simulating this scenario and proposed a large number of niching methods for solving those problems. However, factors causing the difference in attractiveness between local optima are often coupled in existing benchmark problems, which makes it hard to clarify the primary contributors. In addition, niching methods are carried out using a combination of several niching techniques and reproduction operators, which enhances the difficulty of identifying the essential effects of different niching techniques. To obtain an in-depth understanding of the above issue, thus offering actionable insights for optimization tasks challenged by the multimodality, this paper uses continuous optimization as an entry point and focuses on analyzing differential behaviors of EC methods across different basins of attraction. Specifically, we quantitatively investigate the independent impacts of three features of basins of attraction via corresponding benchmark scenarios generated by Free Peaks. The results show that the convergence biases induced by the difference in distribution only occur in EC methods with less uniform reproduction operators. On the other hand, convergence biases induced by differences in size and average fitness, both of which equate to the difference in size of superior region, pose a challenge to any EC method driven by objective functions. As niching methods limit survivor selection to specified neighborhoods to mitigate the latter biases, we abstract five niching techniques from these methods by their definitions of neighborhood for restricted competition, thus identifying key parameters that govern their efficacy. Experiments confirm these parameters’ critical roles in reducing convergence biases. Full article
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15 pages, 954 KB  
Article
Assessing the Post-Brief-Storage Fruit Quality and Sensory Characteristics of Old, Local Apple Cultivars from the Carpathian Basin
by Gitta Ficzek, Sherif Mehmeti, Géza Bujdosó, Ágnes Magyar and Gergely Simon
Plants 2025, 14(13), 2005; https://doi.org/10.3390/plants14132005 - 30 Jun 2025
Viewed by 460
Abstract
Local apple (Malus x domestica Borkh.) cultivars with tolerance to environmental stress factors must be re-evaluated. While the cultivation of apple trees has a long-standing tradition in Hungary, only a handful of cultivars are produced on a large scale, reflecting a trend [...] Read more.
Local apple (Malus x domestica Borkh.) cultivars with tolerance to environmental stress factors must be re-evaluated. While the cultivation of apple trees has a long-standing tradition in Hungary, only a handful of cultivars are produced on a large scale, reflecting a trend in global apple production. The most commonly cultivated apple cultivars worldwide include ‘Golden Delicious’, ‘Red Delicious’, ‘Gala’, ‘Fuji’, and ‘Granny Smith’ (with ‘Jonagold’ and ‘Idared’ being significant in Europe). As a result, genetic diversity among apple cultivars has decreased significantly, which has increased the risk of epidemics if a new pathogen appears. Nonetheless, old and local apple cultivars of the Carpathian Basin have adapted well to Hungarian environmental stress factors and pathogens and seem tolerant to them. In this study, fruit analyses and consumer evaluations of eighteen old, local apple cultivars were conducted. Various physicochemical parameters, such as fruit mass, firmness, total soluble solid content, and total acid content, as well as the content of some biological active compounds, including polyphenol content, antioxidant capacity (FRAP), and pectin content, were determined. Additionally, a consumer evaluation was carried out. Based on the results, most of the old, local apple cultivars exhibit high fruit quality and offer considerable health benefits. The proportion of biologically active compounds in these cultivars is equal to or higher than that in the reference cultivar ‘Watson Jonathan’. Based on the excellent fruit quality and consumer preferences, the ‘Harang alma’ (an attractive fruit exhibiting high FRAP values) and ‘Marosszéki piros’ (with firm flesh and a high pectin content and being particularly tasty) cultivars are recommended for backyard gardens. Full article
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23 pages, 10002 KB  
Article
Post-Mining Hazard Management of the Former Gardanne Coal Basin (France): Feedback of 17 Years of Microseismic Monitoring
by Isabelle Contrucci, Jannes L. Kinscher, Kévin Delage and Emmanuelle Klein
Mining 2025, 5(2), 35; https://doi.org/10.3390/mining5020035 - 6 Jun 2025
Viewed by 866
Abstract
The former Provence coal basin, closed since 2003, has been monitored by a microseismic network since 2008. The objective is to detect the precursor signs of a brittle subsidence that would be caused by the collapse of the old underground mining works. Since [...] Read more.
The former Provence coal basin, closed since 2003, has been monitored by a microseismic network since 2008. The objective is to detect the precursor signs of a brittle subsidence that would be caused by the collapse of the old underground mining works. Since the start of monitoring, no subsidence has affected the risk areas, and nearly 4000 events with a local magnitude between −3 < ML < 3 have been recorded. One sector in particular, called the Fuveau swarm, located outside the risk zones and therefore outside the brittle subsidence hazard zones, has attracted attention since 2012 because it was the subject of several seismic episodes felt in 2010, 2012, 2014, late 2016–early 2017, and August 2017. Since 2017, it has been established that the observed seismicity cannot be explained only by instability phenomena in the old mining works. The most likely hypothesis is that of the remobilization of faults hydraulically connected to the mining works, with seismic activity that is closely linked to variations in the groundwater level, which are themselves influenced by pumping and effective rainfall. This paper shows, through multiplet analysis method of the seismic data recorded by the monitoring network stations, that part of the seismicity in the monitoring areas is also due to the reactivation of tectonic faults. This conclusion is based on the concordance between the location of the multiplets and the orientation of the main faults mapped in the studied areas, as well as on the fact that the strongest events belong to these multiplets. This finding underscores the need to integrate fault reactivation into seismic monitoring strategies, beyond the current focus on mining-induced instabilities. This conclusion leads us to recommend revising the list of post-mining hazards, as post-mining seismic risk is often overlooked in many European regulations. Full article
(This article belongs to the Special Issue Post-Mining Management)
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19 pages, 1612 KB  
Article
Exploring Dynamic Behavior in a Competition Duopoly Game Based on Corporate Social Responsibility
by A. A. Elsadany, Abdullah M. Adawi and A. M. Awad
Computation 2025, 13(6), 131; https://doi.org/10.3390/computation13060131 - 2 Jun 2025
Viewed by 480
Abstract
This study investigates dynamic behaviors within a competition Cournot duopoly framework incorporating consumer surplus, and social welfare through the bounded rationality method. The distinctive aspect of the competition game is the incorporation of discrete difference equations into the players’ optimization problems. Both rivals [...] Read more.
This study investigates dynamic behaviors within a competition Cournot duopoly framework incorporating consumer surplus, and social welfare through the bounded rationality method. The distinctive aspect of the competition game is the incorporation of discrete difference equations into the players’ optimization problems. Both rivals seek to achieve optimal quantity outcomes by maximizing their respective objective functions. The first firm seeks to enhance the average between consumer surplus and its profit, while the second firm focuses on its profit optimization with a social welfare component. The game map features four fixed points, with one being the Nash equilibrium point at the intersection of marginal objective functions. Our analysis explores equilibrium stability, dynamic complexities, basins of attraction, and the emergence of chaos through double routes via flip bifurcation and Neimark-Sacker bifurcations. We observe that increased adjustment speeds can destabilize the system, leading to a richness of dynamic complexity. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems—2nd Edition)
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24 pages, 5324 KB  
Article
Analysis of a Novel Amplitude-Controlled Memristive Hyperchaotic Map and Its Utilization in Image Encryption
by Wenfeng Yang, Lingyun Yang, Jian Liu, Rong Li, Yongtao Wang, Ning Chen and Zhaochuan Hu
Sensors 2025, 25(11), 3388; https://doi.org/10.3390/s25113388 - 28 May 2025
Cited by 1 | Viewed by 464
Abstract
In this paper, a global amplitude-controlled discrete hyperchaotic memristive map is designed utilizing the hyperbolic tangent function. This map exhibits fixed points arranged in a line along the y-axis, and the stability distributions of these fixed points are delineated based on variations [...] Read more.
In this paper, a global amplitude-controlled discrete hyperchaotic memristive map is designed utilizing the hyperbolic tangent function. This map exhibits fixed points arranged in a line along the y-axis, and the stability distributions of these fixed points are delineated based on variations in both the initial conditions of the map and the parameter plane. The dynamic characteristics of the map were examined through the analysis of its 2D dynamics and the largest Lyapunov exponent (LE) distribution. The existence of multistability was robustly confirmed through a comprehensive analysis of the basin of attraction, the spectra of LE that depend on initial values, bifurcation diagrams, and trajectory plots. Additionally, the amplitude of the map can be adjusted both globally and locally through manipulation of the non-bifurcation parameter. Subsequently, a digital circuit powered by a microcontroller was designed to embody the map. In comparison to recent maps, the newly devised map exhibits superior efficacy in the realm of image encryption applications. Full article
(This article belongs to the Section Sensing and Imaging)
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23 pages, 633 KB  
Article
On the Convergence Order of Jarratt-Type Methods for Nonlinear Equations
by Shobha M. Erappa, Suma P. Bheemaiah, Santhosh George, Kanagaraj Karuppaiah and Ioannis K. Argyros
Axioms 2025, 14(6), 401; https://doi.org/10.3390/axioms14060401 - 24 May 2025
Viewed by 450
Abstract
The order of convergence for Jarratt-type methods in solving nonlinear equations is determined without relying on Taylor expansion. Unlike previous studies, we depend solely on assumptions about the derivatives of the involved operator up to the second order. The proof presented in this [...] Read more.
The order of convergence for Jarratt-type methods in solving nonlinear equations is determined without relying on Taylor expansion. Unlike previous studies, we depend solely on assumptions about the derivatives of the involved operator up to the second order. The proof presented in this paper is independent of the Taylor series expansion, thereby reducing the need for assumptions about derivatives of higher order of the involved operator and enhancing the applicability of these methods. The method’s applicability is broadened by employing the concept of generalized conditions in local convergence analysis and majorizing sequences in semi-local analysis. This study includes numerical examples and basins of attraction for the methods. Full article
(This article belongs to the Section Mathematical Analysis)
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