Chaos Solitons & Fractals最新文献

{"title":"Local bifurcation behavior, chaos, and oblique travelling wave structures in the (2 + 1)-dimensional chiral Schrödinger equation with beta derivative","authors":"K.M. Abdul Al Woadud ,&nbsp;Dipankar Kumar ,&nbsp;Aminur Rahman Khan","doi":"10.1016/j.chaos.2025.117726","DOIUrl":"10.1016/j.chaos.2025.117726","url":null,"abstract":"<div><div>Qualitative analysis in mathematical modeling plays a pivotal role in understanding the dynamical behavior of the complex systems, making it a cornerstone of research in nonlinear sciences. The bifurcation method is a crucial tool to investigate dynamical properties, enabling researchers to explore and characterize structural changes in orbits within nonlinear dynamical systems. By applying the bifurcation method to the (2 + 1)-dimensional chiral nonlinear Schrödinger (NLS) equation with beta-derivative, this study investigates phase portrait bifurcations, chaotic dynamics, and examines sensitivity and multi-stability properties of the system. Initially, phase portrait bifurcations are analyzed graphically by determining the equilibrium points and assessing their stability using the Jacobian matrix. The study demonstrates how the equilibrium points evolve as different angles are varied, revealing the system's dynamic nature under changing conditions. Hereafter, by introducing a perturbation term to the planar system, chaotic patterns are identified through 2D and 3D phase portraits, time series analysis, Lyapunov exponents, and Poincaré maps. The system's sensitivity and multi-stability are further explored using the Runge-Kutta method, showing strong dependence on initial conditions. Meanwhile, the planar dynamical system approach applied to the beta-derivative chiral NLS model yields various soliton solutions, including periodic, bright, and dark solitons. All generated solutions are shown to be novel in terms of their fractionality, wave propagation behavior, and the influence of free parameters, as well as the application of the methods. Therefore, this study provides deeper insight into the dynamics of the β-derivative chiral NLS model and emphasizes its broader significance in understanding nonlinear phenomena.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117726"},"PeriodicalIF":5.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigations on dynamics of isomeric bound multi-pure-quartic solitons in mode-locked fiber laser","authors":"Ying Han ,&nbsp;Yujing Wu ,&nbsp;Yihu Xu ,&nbsp;Bo Gao","doi":"10.1016/j.chaos.2025.117727","DOIUrl":"10.1016/j.chaos.2025.117727","url":null,"abstract":"<div><div>Pure-quartic solitons (PQSs) have recently attracted growing research interest due to their energy-width scaling characteristics, which expands the understanding of pure-high-order dispersion solitons in nonlinear systems. Additionally, bound solitons are the most representative manifestations of the particle-like nature of solitons and have inspired numerous light-matter analogies. While previous studies have predominantly focused on bound PQSs with equal time separation, reports on isomeric bound multi-PQSs featuring unequal time separation remain scare. Herein, we numerically investigate the dynamics of isomeric bound multi-PQSs associated with the periodic filter effect in mode-locked fiber laser. By modulating the intra-cavity phase delay to achieve distinct periodic filter properties, we obtained isomeric bound multi-PQSs with temporal creeping, spectral breathing, and time walk-off. Analyses of the time-domain, frequency-domain, and pulse energy characteristics reveal that the periodic variations of bound multi-PQSs are linked to intensity exchange and intra-cavity periodic filter effect. These findings imply that PQS fiber lasers may also serve as promising platforms for manipulating the properties of isomeric bound multi-solitons.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117727"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical behaviors of a stochastic SIS model on Metapopulation Networks with Markovian switching","authors":"Wenjun Jing ,&nbsp;Xiaochun Cao ,&nbsp;Juping Zhang","doi":"10.1016/j.chaos.2025.117736","DOIUrl":"10.1016/j.chaos.2025.117736","url":null,"abstract":"<div><div>Considering the impacts of human mobility and telegraph noise on infectious disease transmission, a stochastic SIS model on metapopulation networks with Markovian switching is formulated. By constructing a Lyapunov function, the existence of a unique global positive solution to the model is proved. Moreover, we derive sufficient conditions for the extinction and persistence in mean of the infectious disease. The results reveal the important role of the stationary distribution of Markov chain in determining the threshold conditions. Furthermore, numerical simulations indicate that environmental switching can lead to the potential for multi-wave spread of infectious diseases. When the environment switches at a speed of logarithmic scale, the speed of environmental switching is not directly related to the thresholds, but affects the temporal fluctuations of the epidemic. The slower the speed of environmental switching, the lower the frequency of fluctuation, but the larger the fluctuation amplitude of epidemic spreading. Our work contributes to enrich the theoretical analysis of epidemic dynamics on metapopulation networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117736"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neighborhood centroid opposition-based flood algorithm for optimizing fractional-order PID control in nonlinear heat exchanger dynamics","authors":"Davut Izci ,&nbsp;Erdal Eker ,&nbsp;Serdar Ekinci ,&nbsp;Mohit Bajaj ,&nbsp;Vojtech Blazek ,&nbsp;Lukas Prokop","doi":"10.1016/j.chaos.2025.117729","DOIUrl":"10.1016/j.chaos.2025.117729","url":null,"abstract":"<div><div>This study presents a novel neighborhood centroid opposition-based flood algorithm (NCO-FLA) for optimizing fractional-order proportional-integral-derivative (FOPID) controllers aimed at precise temperature regulation in nonlinear shell-and-tube heat exchanger systems. By integrating opposition-based learning (OBL) and neighborhood centroid mechanisms into the conventional flood algorithm (FLA), the proposed NCO-FLA significantly improves global search efficiency and mitigates premature convergence in high-dimensional parameter spaces. The FOPID controller, with its five tunable parameters, provides a more flexible and robust framework than traditional PID structures, especially under nonlinear and dynamic conditions commonly encountered in industrial heat exchange processes. Extensive simulations conducted in MATLAB/Simulink demonstrate that NCO-FLA outperforms benchmark metaheuristic algorithms, including the marine predators algorithm (MPA), reptile search algorithm (RSA), catch fish optimization algorithm (CFOA), and the original FLA as well as classical algorithms such as differential evolution (DE), particle swarm optimization (PSO), evolution strategy with covariance matrix adaptation (CMA-ES), DE variants with linear population size reduction (L-SHADE) and NCO-PSO. Quantitative results show that he proposed NCO-FLA achieved 10–15 % lower ITAE values compared to the other optimizers, confirming its enhanced control accuracy and convergence stability. The proposed NCO-FLA also exhibited a smoother and faster convergence trend compared to other algorithms, as confirmed by the convergence profiles, and achieved the lowest standard deviation (0.9183), indicating superior consistency and reliability. Additionally, the NCO-FLA-tuned FOPID controller achieves zero overshoot, near-zero steady-state error, and significantly shorter rise (5.16 s) and settling times (19.05 s). Statistical significance was confirmed through Friedman and Wilcoxon signed-rank tests, as well as Mann-Whitney <em>U</em> test where all <em>p</em>-values were below 0.05, affirming the superiority and robustness of the proposed method. These findings underscore the algorithm's strong potential for real-world deployment in complex thermal systems where high accuracy, stability, and adaptive control are critical. The proposed NCO-FLA represents a promising advancement in metaheuristic optimization for industrial control systems. Future work will focus on integrating the algorithm with machine learning models and evaluating its performance in large-scale, real-time environments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117729"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling and analysis of human chaotic dynamics based on clinical data","authors":"Yuxi Liu,&nbsp;Fuzhong Nian","doi":"10.1016/j.chaos.2025.117708","DOIUrl":"10.1016/j.chaos.2025.117708","url":null,"abstract":"<div><div>Based on the detection data of bioelectrical signals of the twelve meridians collected clinically, this paper constructs a five-dimensional nonlinear dynamic equation system that conforms to the characteristics of traditional Chinese medicine (TCM) theory by integrating the “mechanism of generation, restraint, and transformation” of the five elements theory on the basis of the classic Lotka–Volterra model. Through the two-level mapping relationship of acupoints-meridians-five elements, the quantitative characterization of the characteristic values of the five-elements, namely metal (J), wood (M), water (S), fire (H), and earth (T), is achieved. This paper proposes a PSO-GA integrated optimization strategy to identify the parameters of the system, overcoming the problem that parameter fitting of high-dimensional nonlinear systems is prone to fall into local optima. By calculating the Lyapunov exponents and the fractal dimension of the attractor, and plotting the bifurcation diagram and phase portrait, the chaotic characteristics and evolution laws of the human five elements system in healthy, sub-healthy, and diseased states are verified. The research shows that the healthy state exhibits chaotic characteristics (Lyapunov exponents <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>2596</mn><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>1881</mn></mrow></math></span>); the chaotic characteristics of the sub-healthy state are weakened (the maximum positive exponent <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>0842</mn></mrow></math></span>); the diseased state shows non-chaotic behavior (all negative exponents). This research proposes an effective new method for evaluating human health status by combining meridian detection data analysis. It provides new modeling ideas for modernization and scientific advancement of TCM theory, reveals the nonlinear regulation mechanism of the five elements chaotic system and its potential role in health evolution, and also provides a methodological reference for health assessment and early disease prediction based on dynamic characteristics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117708"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear disruption of integration-segregation balance in task-based fMRI brain networks of depression","authors":"Wenzheng Ma ,&nbsp;Yu Wang ,&nbsp;Ningxin Ma ,&nbsp;Hongbing Xiao","doi":"10.1016/j.chaos.2025.117733","DOIUrl":"10.1016/j.chaos.2025.117733","url":null,"abstract":"<div><div>Depression is often accompanied by impairments in reward-punishment feedback processing, yet the underlying complex-system mechanisms of brain functional networks remain unclear. Complex network theory provides a novel paradigm for characterizing the dynamics of integration and segregation in brain networks and for uncovering nonlinear topological alterations in psychiatric disorders. In this study, we constructed brain functional networks of patients with depression and healthy controls based on task-related fMRI data from a gambling reward-punishment paradigm. Using graph-theoretical and complex network approaches, we evaluated key topological measures, including global efficiency, local efficiency, and small-world properties, and further examined the coupling between network topology and behavioral reaction times. Individuals with depression exhibited significantly reduced network integration capacity, manifested by decreased global and local efficiency, which progressively worsened with clinical severity. In contrast, small-world properties in certain regions showed relative enhancement, which may reflect local reorganization or compensatory tendencies within the network rather than a definitive adaptive mechanism. Moreover, the degree of topological disruption was negatively correlated with reaction time, revealing a coupling between cognitive slowing and information transfer efficiency in complex networks. Overall, depression in reward-punishment contexts is characterized by a nonlinear disruption of the integration-segregation balance of brain networks, with impaired global transmission efficiency and adaptive modulation of local modularity and small-world organization. The results not only delineate the multilayered abnormalities of brain networks in depression but also indicate that complex network theory may provide novel topological biomarkers for the diagnosis and prediction of psychiatric disorders.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117733"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145732366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Restabilization of spiral waves and suppression of Doppler and Eckhaus instabilities by circularly polarized electric fields","authors":"Hongling Xu ,&nbsp;Debei Pan","doi":"10.1016/j.chaos.2025.117730","DOIUrl":"10.1016/j.chaos.2025.117730","url":null,"abstract":"<div><div>The onset of fibrillation is closely associated with the instability of spiral waves in cardiac tissue. Understanding the interaction between spiral wave instabilities, system properties, and control mechanisms has been a key research focus. In this study, a reaction-diffusion model is used to demonstrate that both Doppler and Eckhaus instabilities of spiral waves can be suppressed and restabilized through the application of circularly polarized electric fields (CPEF). Numerical simulations show that early intervention with CPEF, before the onset of these instabilities, significantly enhances the suppression of spiral wave progression into spatiotemporal chaos. The intensity, frequency and timing of CPEF application are crucial factors in determining the success of control. Compared to direct current (DC) and alternating current (AC) electric fields, the unique rotating characteristics of CPEF proves to be particularly effective in stabilizing spiral waves, offering a potential mechanism for suppressing Doppler and Eckhaus instabilities. These findings could have potential implications for clinical strategies in managing cardiac arrhythmias.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117730"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Community detection in complex networks using vertex cover and an adaptive community transformer engine","authors":"Fahimeh Dabaghi-Zarandi ,&nbsp;Pouria HosseiniDokht ,&nbsp;Asieh Ghanbarpour ,&nbsp;Zohreh Davarzani","doi":"10.1016/j.chaos.2025.117714","DOIUrl":"10.1016/j.chaos.2025.117714","url":null,"abstract":"<div><div>In recent years, the study of complex networks, such as biological, social, and economic systems, has attracted significant attention due to the complicated interactions among their entities. Community detection plays a key role in uncovering the hidden structure of these networks by dividing them into distinct subgroups, or communities. Research in community detection aims to extract relatively distinct sub-networks, known as communities, from the complex network structure to better understand its topology and functional organization. In this paper, we propose a novel community detection method based on a defined architecture composed of a Data Repository and three main components: Pre-Processing, Primary Communities Composition, and an Adaptive Community Transformer. In the first component, similarity measures are identified and stored, and appropriate weights are assigned to network links. The second component identifies significant network nodes using vertex cover along with the defined measures and weights. Primary community structures are then composed by considering vertex cover nodes as the centers of communities. After refining the primary community structure, an adaptive engine in the third component decides whether to merge or split communities to achieve the optimal community structure. We evaluate our method across various network sizes–small, medium, and large–including both real-world and artificial network scenarios. Compared to other approaches, the community structures detected by our method are size-independent and demonstrate strong evaluation metrics across all network types, especially in large-scale networks. Therefore, our proposal effectively detects community structures that resemble those found in real-world networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117714"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Advancing from 2m-sets of triangular functions to 3m-sets of parabolic functions: Direct solutions for integral equations","authors":"Bricio Cuahutenango-Barro ,&nbsp;Luis X. Vivas-Cruz ,&nbsp;Alfredo González-Calderón ,&nbsp;M.A. Taneco-Hernández ,&nbsp;Ana Teresa Mendoza-Rosas","doi":"10.1016/j.chaos.2025.117722","DOIUrl":"10.1016/j.chaos.2025.117722","url":null,"abstract":"<div><div>Orthogonal functions have long been fundamental in mathematical modeling and analysis, particularly for their adaptability to computational environments. With the increasing complexity of digital technologies, piecewise orthogonal functions have gained prominence for their efficiency in simplifying differential and integral equations. This work introduces a novel class of <span><math><mrow><mn>3</mn><mi>m</mi></mrow></math></span>-sets of piecewise orthogonal parabolic (quadratic) functions (PFs). These functions decompose differential and integral equations into computationally manageable components, offering improvements in accuracy compared to the existing <span><math><mrow><mn>2</mn><mi>m</mi></mrow></math></span>-sets and <span><math><mrow><mn>1</mn><mi>m</mi></mrow></math></span>-set of piecewise orthogonal linear and constant functions, respectively. We investigate the mathematical properties of these PFs, develop operational matrices for definite integrals, and demonstrate their effectiveness in solving second-kind Volterra integral equations. As we have shown, the derived formula can be useful in cases where kernels with fractional memory are involved. This new methodology enables the transformation of equations into explicit algebraic forms, eliminating the need for traditional integration methods and offering substantial computational benefits. The approach enhances both the precision and applicability of numerical solutions across various fields of applied mathematics and engineering, expanding the toolkit available to researchers and practitioners.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117722"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Resilience analysis of multi-level highway networks under disruptions","authors":"Xuan Zhang,&nbsp;Shuaijie Zhang,&nbsp;Jinjun Tang,&nbsp;Lipeng Hu,&nbsp;Lin Qin","doi":"10.1016/j.chaos.2025.117728","DOIUrl":"10.1016/j.chaos.2025.117728","url":null,"abstract":"<div><div>The measurement of resilience in regional highway networks is crucial for ensuring regional safety and efficiency. This study investigates the topological and functional resilience of sub-networks and multi-level highway networks under various disruption scenarios. In particular, functional resilience is evaluated by incorporating the traffic characteristics of the highway network. Furthermore, the study explores the optimal recovery sequence of failed edges to maximize overall network resilience. To validate the proposed approach, we apply highway network and volume data from Hunan Province, China. The results demonstrate that multilevel networks exhibit greater resilience against disruptions compared to individual sub-networks. Additionally, the findings indicate that functional resilience is more vulnerable to disruptions and exhibits lower recovery effectiveness than topological resilience. These insights provide valuable guidance for stakeholders, enhancing their understanding of transportation network resilience and offering a practical reference for the development of resilience strategies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"204 ","pages":"Article 117728"},"PeriodicalIF":5.6,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145732367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}