Chaos Solitons & Fractals最新文献

{"title":"Multiplicative Riemann–Liouville fractional integrals and derivatives","authors":"Umut Bas,&nbsp;Abdullah Akkurt,&nbsp;Aykut Has,&nbsp;Huseyin Yildirim","doi":"10.1016/j.chaos.2025.116310","DOIUrl":"10.1016/j.chaos.2025.116310","url":null,"abstract":"<div><div>This study explores the connections between fractional calculus, a field that has recently garnered significant research interest, and multiplicative analysis. The introduction provides a comprehensive overview of the historical development and foundational concepts of these areas. The preliminary section outlines key definitions and illustrative examples from multiplicative analysis. The research derives the multiplicative representations of the gamma and beta functions and examines their fundamental properties. Furthermore, generalizations of integrals and derivatives within the framework of multiplicative analysis are formulated, accompanied by explicit formulas for multiplicative integrals and derivatives. Finally, fractional-order multiplicative integral derivatives for selected functions are introduced and visualized through graphical representations, highlighting their practical implications.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116310"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776566","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":"Quantum-inspired feature extraction model from EEG frequency waves for enhanced schizophrenia detection","authors":"Ateke Goshvarpour","doi":"10.1016/j.chaos.2025.116401","DOIUrl":"10.1016/j.chaos.2025.116401","url":null,"abstract":"<div><h3>Purpose</h3><div>Schizophrenia diagnosis remains challenging due to the reliance on subjective clinical assessments and the lack of robust, objective biomarkers. Current neuroimaging methods are often expensive, time-consuming, and may lack specificity, highlighting the need for the development of scalable and accurate diagnostic tools. This study investigates the feasibility of using electroencephalogram (EEG) frequency waves as biomarkers for the detection of schizophrenia, employing a quantum-based feature extraction methodology. The primary objective of this research is to develop an advanced detection methodology that integrates quantum-based feature extraction with sophisticated channel and feature selection techniques. This approach aims to enhance the accuracy and reliability of schizophrenia diagnosis by identifying the most informative EEG channels and features for classification purposes.</div></div><div><h3>Methods</h3><div>First, EEG frequency bands are extracted using the wavelet packet decomposition technique. Next, three channel selection algorithms prioritize channels based on the highest variance, power, and lowest coefficient of variation. The methodology involves applying discrete quantum analysis for feature extraction, followed by the extraction of statistical measures to create a comprehensive feature set. Feature selection is performed using Minimum Redundancy Maximum Relevance (mRMR) and ReliefF to retain the most relevant and non-redundant features. These features are then analyzed using various classification models, including AdaBoost, Support Vector Machine (SVM), Decision Tree (DT), and K-Nearest Neighbors (KNN).</div></div><div><h3>Results</h3><div>The findings of the study underscore the superior performance of the mRMR method when combined with variance and coefficient of variation-based channel selection techniques, particularly in the β and θ frequency bands. The KNN classifier achieves 100 % accuracy, sensitivity, and F1 score for the δ, θ, SMR, and β waves under optimal conditions. The mRMR method attains an average accuracy of 92.80 % for δ waves, 95.20 % for θ waves, 92.59 % for SMR waves, and 94.26 % for β waves when used in conjunction with coefficient of variation-based channel selection. In contrast, the ReliefF method demonstrates suboptimal performance in higher frequency bands, such as the γ wave, achieving an average accuracy of only 51.55 % when paired with variance-based channel selection.</div></div><div><h3>Conclusion</h3><div>The proposed methodology presents a promising approach to improving the accuracy and reliability of schizophrenia diagnosis.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116401"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776574","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":"Conditional McKean–Vlasov stochastic differential equations driven by fractional Brownian motions","authors":"Guangjun Shen,&nbsp;Jiangpeng Wang","doi":"10.1016/j.chaos.2025.116348","DOIUrl":"10.1016/j.chaos.2025.116348","url":null,"abstract":"<div><div>In this paper, we are concerned with a class of McKean–Vlasov stochastic differential equations with Markovian regime-switching driven by fractional Brownian motions with Hurst parameter <span><math><mrow><mi>H</mi><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. We first obtain the existence and uniqueness theorem for solutions of the concerned equations under the non-Lipschitz conditions. Second, we establish the propagation of chaos for the associated mean-field interaction particle systems with common noise and provide an explicit bound on the convergence rate. At last, an averaging principle is investigated with respect to two time-scale conditional McKean–Vlasov stochastic differential equations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116348"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776572","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 two competing infectious diseases in a metropolitan contact network","authors":"Yunzhu Xiao ,&nbsp;Wenjie Li ,&nbsp;Yanyi Nie ,&nbsp;Jiayi Song ,&nbsp;Manrui Zhao ,&nbsp;Zengping Zhang ,&nbsp;Xiaoyang Liu ,&nbsp;Yong Tang ,&nbsp;Wei Wang","doi":"10.1016/j.chaos.2025.116282","DOIUrl":"10.1016/j.chaos.2025.116282","url":null,"abstract":"<div><div>Infectious diseases rarely spread in isolation, and the competing spreading of multiple diseases widely exists. However, existing studies on the dynamics of competing infectious diseases typically rely on networked populations, lacking systematic research on specific metropolitan areas. This study proposes a competing infectious disease model to describe two competing infectious diseases spreading in metropolitan areas. An analytical framework of the theory is first developed to characterize this high-dimension system though expanded mean-field theory. To describe this spreading process more conveniently, we propose a dimension-reduction method to reduce the system complexity. Finally, we use an age-contact data-driven approach to simulate the spreading of two competing infectious diseases in metropolitan cities like New York. The results validate our dimension-reduction method’s reliability, allowing us to describe the high-dimension system through a one-dimensional equation. We observed three main scenarios of competing disease spreading, i.e., neither disease can break out, one disease dominates, while the other is suppressed, and the two diseases coexist throughout the spreading. Moreover, our simulations show that the workplace favours specific diseases with stronger spreading capabilities than other settings.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116282"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776568","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":"Stochastic FitzHugh–Nagumo neuron model with Gamma distributed delay kernel","authors":"Kuldeep Tiwari,&nbsp;Dilip Senapati","doi":"10.1016/j.chaos.2025.116378","DOIUrl":"10.1016/j.chaos.2025.116378","url":null,"abstract":"<div><div>The FitzHugh–Nagumo (FHN) model is an efficient and biologically plausible model for simulating neuronal dynamics. However, it lacks any inherent capability to appropriately integrate memory effects. In this study, a non-Markov stochastic neuron model is formulated as an extension of the FHN model by incorporating Gamma distributed delay kernel as the form of memory in a recovery variable. Additionally, we propose an enhanced framework to incorporate neuronal noise into this model, further improving its ability to describe the propagation of action potential spikes along axons. We simulate the action potential signals recorded from the rat cortex by employing the modified version of the FHN model. This is done by constructing the input impulse signal from the recorded action potential data based on the time and quality of the action potential. This impulse signal is fed as input in the modified FHN model resulting in the replication of firing patterns of rat cortex, effectively replicate the action potential signals along with incorporating the inherent noise present in the recordings. This demonstrates the ability of the modified FHN model to accurately capture the dynamics of neuronal activity.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116378"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776570","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":"Bifurcations of a Leslie-type model with herd behavior and predator harvesting","authors":"Zhifei Guo,&nbsp;Haiying Yang","doi":"10.1016/j.chaos.2025.116327","DOIUrl":"10.1016/j.chaos.2025.116327","url":null,"abstract":"<div><div>It was demonstrated that the herd behavior in prey, described by a square root functional response, induces a Hopf bifurcation in the Leslie-type predator–prey model. This paper is devoted to discussing bifurcations of the same model, but with constant-rate predator harvesting. We show that the system exhibits complicated bifurcations driven by the predator harvesting. More concretely, we first prove that the system has at most two equilibria, which consist of a saddle and either a focus or a node, respectively. Then we verify that the system undergoes the attracting and repelling Bogdanov–Takens bifurcations of codimension two. Additionally, we show that a degenerate Hopf bifurcation of codimension three can also occur at a weak focus. The theoretical findings, which are further illustrated by numerical simulations, reveal that the two populations can coexist periodically under constant-rate predator harvesting.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116327"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776573","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":"Time series analysis of wildfire propagation in Chile: A complex networks approach","authors":"Iván Gallo-Méndez ,&nbsp;Jaime Clark ,&nbsp;Denisse Pastén","doi":"10.1016/j.chaos.2025.116347","DOIUrl":"10.1016/j.chaos.2025.116347","url":null,"abstract":"<div><div>Wildfires are a recurrent and devastating phenomenon that has expanded in Chile and various places worldwide, with complex propagation patterns influenced by environmental, climatic, and anthropogenic factors. In this study, we employ a complex network framework to analyze the temporal and spatial dynamics of fire propagation throughout Chile. Using publicly available data on wildfires, including their locations and dates of occurrence, we map the position and timing of events onto an undirected spatial complex network to characterize fire propagation in Chile’s central and southern zones from a multifractal point of view. We construct a time series associated with the connectivity of nodes, where each event is assigned to a node by position match. Traversing the network sequentially, based on the date and time of the events, generates the connectivity time series, which captures spatiotemporal information. Our analysis demonstrates that the graph exhibits hallmark complexity features. In addition, through an analysis of the connectivity time series, we uncover the multifractal nature of the system. In particular, we show that the central zone exhibits a more remarkable persistence of multifractal behavior than the southern zone, which could provide insights into the underlying dynamics of the system and be valuable for identifying regions with heightened structural or temporal complexity. We expect our findings will contribute to understanding the spatial heterogeneity of fire distribution in Chile and serve as a precedent for future research.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116347"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776569","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":"Firing modes of a memristive complex-valued FHN neuron","authors":"Huaqing Nie ,&nbsp;Jian Liu ,&nbsp;Dan Wang ,&nbsp;Fangfang Zhang ,&nbsp;Wenjing Wang","doi":"10.1016/j.chaos.2025.116372","DOIUrl":"10.1016/j.chaos.2025.116372","url":null,"abstract":"<div><div>Memristors have been extensively integrated into neurons as key elements for emulating electromagnetic radiation (EMR). The complex firing patterns triggered by external magnetic field is a hot topic in neuronal dynamics. By integrating a specially designed memristor into a complex-valued FitzHugh–Nagumo (CV-FHN) neuron model to emulate external magnetic induction current, we have developed a novel neuromorphic system. Our findings reveal that hidden scroll-controlled chaotic attractors can be generated from the neuromorphic system through adjustment of the memristor parameter, while the offset of heterogeneous coexisting attractors in the phase space can be boosted by modifying the initial conditions of the memristor. Moreover, the Hamilton energy function of the neuron is calculated by using Helmholtz’s theorem. The results of Hamilton energy analysis indicate that various hidden firing patterns, including hidden chaotic spiking and even hyperchaotic bursting, can be modulated by external stimuli. In this work, the introduction of memristor into CV-FHN neuron significantly enhances the chaos complexity of neuronal firing dynamics of the original neuron. This memristive CV-FHN neuron serves as a promising candidate for constituting large-scale functional neural network.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116372"},"PeriodicalIF":5.3,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143776571","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":"Dynamic analysis of the nonlinear fiber oscillator with fractional-order control in multi-filament fiber winding","authors":"Xinlei Fang ,&nbsp;Jianguo Liang ,&nbsp;Jiaquan Xie ,&nbsp;Zhanchun Chen ,&nbsp;Ting Wu ,&nbsp;Jianglin Liu","doi":"10.1016/j.chaos.2025.116385","DOIUrl":"10.1016/j.chaos.2025.116385","url":null,"abstract":"<div><div>This work aims to investigate the dynamic behavior of the carbon fiber oscillator in the winding process of the novel multi-filament fiber winding equipment for high-pressure vessels, employing an improved fractional-order controller. Specifically, a coupling suppression fractional-order PD (CS-FOPD) control strategy is proposed for the two-degree-of-freedom carbon fiber oscillator. The multiple-scales method is employed to analyze the primary resonance of the system and derive the steady-state amplitude and phase solutions. The stability of the system is assessed using the Routh-Hurwitz criterion, and the analytical solutions are validated through numerical simulations. Furthermore, numerical simulations are conducted to investigate the effects of CS-FOPD control on the amplitude-frequency characteristics, controller performance, multi-stable phenomenon, attraction domain structure, and global bifurcation behavior of the system under varying system parameters. In the absence of coupling suppression strategy, the primary-superharmonic resonance characteristics are analyzed using the multiple-scales method, and stability is evaluated via Lyapunov's first method. The nonlinear dynamics of the system are further explored through amplitude-frequency response curves and attraction domain evolution. Finally, the Melnikov method is employed to calculate the distance between stable and unstable manifolds, providing an analytical prediction of the onset of chaos. The main obtained simulation results showed the excellent performance of the proposed control strategy and the evolution of the system's dynamic characteristics. By analyzing the nonlinear dynamics of the system under the proposed control strategy, this study provides key insights for optimizing the stability and performance of the novel multi-filament carbon fiber winding equipment.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116385"},"PeriodicalIF":5.3,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759621","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":"Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model","authors":"Shaohui Yan,&nbsp;Xinyu Wu,&nbsp;Jiawei Jiang","doi":"10.1016/j.chaos.2025.116337","DOIUrl":"10.1016/j.chaos.2025.116337","url":null,"abstract":"<div><div>To overcome the limitations of conventional designs for memristive multi-scroll chaotic systems, this paper introduces a novel memristor that relies solely on a single memristor function and a single state variable function to generate both odd and even numbers of double-scroll attractors. This design not only simplifies the memristor structure but also offers a new approach to constructing multi-scroll chaotic systems. The proposed memristor is integrate into a modified Sprott-C system to develop the one-dimensional memristive multi-scroll Sprott-C systems (1D-MMSCS), two-dimensional memristive multi-scroll Sprott-C systems (2D-MMSCS), and the three-dimensional memristive multi-scroll Sprott-C systems (3D-MMSCS). The complex dynamics of these memristive multi-scroll systems are analyzed using equilibrium points, Poincaré maps, bifurcation diagrams, and Lyapunov exponents. Interestingly, the constructed MMSCS exhibits extreme multi-stability, indicating its high sensitivity to initial conditions and enhanced unpredictability. To verify the practical feasibility of the system, it is developed a digital hardware platform based on a Field-Programmable Gate Array (FPGA) and successfully implemented both the 1D-MMSCS and 2D-MMSCS. Finally, leveraging Lyapunov stability theory and predefined-time stability theory, a novel predefined-time sliding mode control scheme (PTSMS) is proposed. This scheme is applied to achieve synchronization in the more complex 3D-MMSCS. Simulation results confirm that the proposed method ensures rapid synchronization and exhibits strong robustness against internal uncertainties and external disturbances.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116337"},"PeriodicalIF":5.3,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759619","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}