Chaos Solitons & Fractals最新文献

{"title":"A novel detection approach of bifurcation-induced tipping points with generalized Ornstein-Uhlenbeck process in finance","authors":"Weijia Chen,&nbsp;Shupei Huang","doi":"10.1016/j.chaos.2025.117257","DOIUrl":"10.1016/j.chaos.2025.117257","url":null,"abstract":"<div><div>Detecting bifurcation-induced tipping points can help prevent the collapse of dynamic financial systems. Current detection methods, such as the Bai and Perron test and the Markov-switching model, identify tipping points based on probabilistic assumptions. However, these conventional methods often fail to capture the complex underlying mechanisms of financial markets. Additionally, traditional methods are less effective when applied to systems affected by internal and external interactions. To address these limitations, we propose an alternative detection method based on the Generalized Ornstein-Uhlenbeck (GOU) process. In this study, we develop a parameter estimation strategy for the bifurcation-induced tipping points detection (BTPD) method in dynamic financial systems. This novel method employs a stochastic differential equation (SDE) governed by the GOU process, providing improved sensitivity to detect transitions. We prove the asymptotic normality and consistency of the parameter estimators under standard regularity conditions. We demonstrate the effectiveness of the BTPD method using data from crude oil futures, other commodity futures, major stock indices and exchange rates. This approach provides a more comprehensive toolkit for anticipating critical transitions in complex financial systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117257"},"PeriodicalIF":5.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217999","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":"Various rational solutions generated from the higher order Kaup–Newell type equation","authors":"Shuwei Xu ,&nbsp;Jingsong He","doi":"10.1016/j.chaos.2025.117286","DOIUrl":"10.1016/j.chaos.2025.117286","url":null,"abstract":"<div><div>The types of soliton interactions, such as weak interactions, strong interactions, stable new local waves and rogue waves, are very rich. Considering the extremely rich soliton type solutions, for example, bright or dark solitons, phase solutions and breather solutions, in the higher order Kaup–Newell type equation which can describe the waves propagation in optical and plasma system, the analysis of the interactions between various solutions is helpful for constructing new solutions and explaining new phenomena. Compared with the previous research results, we mainly focus on the following two aspects: (i) The higher order term plays a unique role in the formation of rational solutions; (ii) The various rational solutions are generated from the synchronized and resonant interactions of multiple solitons. These studies mainly elaborate on the formation of large amplitude waves, such as rogue waves, rational W-shape solitons, and rational dark or bright solitons, in terms of boundary conditions, the number of soliton interactions, spectral parameters and the higher order terms in this equation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117286"},"PeriodicalIF":5.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217992","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":"Integral contractor and conformable fractional differential transform approach to study optimal control, T-controllability and Ulam-Hyer’s-Rassia’s stability for higher-order stochastic system","authors":"Dimplekumar Chalishajar ,&nbsp;Dhanalakshmi Kasinathan ,&nbsp;Ramkumar Kasinathan ,&nbsp;Ravikumar Kasinathan","doi":"10.1016/j.chaos.2025.117310","DOIUrl":"10.1016/j.chaos.2025.117310","url":null,"abstract":"<div><div>The increasing complexity of dynamical systems in science and engineering, particularly those influenced by memory and uncertainty, motivates the study of conformable fractional stochastic differential equations (CFSDEs). These models capture both fractional-order dynamics and stochastic behavior, offering a richer framework than classical approaches. This paper investigates the optimal control, uniqueness, Ulam–Hyers–Rassias stability (UHRS), and trajectory (T)-controllability of mild solutions to CFSDEs with fractional-order initial conditions. The analysis is further extended to coupled CFSDEs and higher-order Sobolev-type systems, where both the governing equations and boundary conditions involve fractional-order terms. Methodologically, stochastic analysis, sequencing techniques, and bounded integral contractors are employed to establish the main results. Unlike earlier studies, the proposed framework avoids reliance on the induced inverse of the controllability operator and does not impose Lipschitz restrictions on nonlinear functions. Grownwall’s inequality is used to derive T-controllability, while Balder’s theorem ensures optimal controllability. In addition, dynamic constraints are expressed in terms of conformable fractional derivatives, and variational methods yield optimality conditions. To support practical implementation, the conformable fractional differential transform (CFDT) method is applied for the numerical modeling of fractional optimal control problems (FOCPs), with illustrative applications demonstrating the effectiveness of the proposed approach.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117310"},"PeriodicalIF":5.6,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217996","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":"Coherent control and shift of exceptional points in micro-ring resonators via resonant frequency through four-level N-type atomic medium","authors":"Fayaz Muhammad,&nbsp;Muhammad Javed","doi":"10.1016/j.chaos.2025.117245","DOIUrl":"10.1016/j.chaos.2025.117245","url":null,"abstract":"<div><div>Coherent control of exceptional points (EPs) through resonant frequency manipulation is a pressing question in the field of non-Hermitian physics. EPs, distinguished by the coalescence of eigenvectors and eigenvalues, possess unusual properties that can be a basis for various applications, including sensitivity enhancement, energy harvesting, and signal processing. The current article explores coherent control, with a focus on the resonant frequency as a key parameter. Resonant frequency plays a significant role in the behavior of EPs. It is possible to control their properties and coherent behavior by adjusting the system’s physical parameters, such as the index of refraction, size of the micro-ring resonators, and material properties, to match the desired resonant frequency. Through this control mechanism, it is possible to tailor the transmission and reflection properties of waves, enhancing or suppressing certain modes, and to modify the sensitivity of the system to external perturbations. The present work may enable us to design novel devices for optical communication, sensing, and signal processing, and it may open possibilities for controlling entanglement and coherence in quantum information processing.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117245"},"PeriodicalIF":5.6,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217877","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":"Augmented regression models using neurochaos learning","authors":"Akhila Henry,&nbsp;Nithin Nagaraj","doi":"10.1016/j.chaos.2025.117213","DOIUrl":"10.1016/j.chaos.2025.117213","url":null,"abstract":"<div><div>This study presents novel Augmented Regression Models using Neurochaos Learning (NL), where <em>Tracemean</em> features derived from the Neurochaos Learning framework are integrated with traditional regression algorithms - <em>Linear Regression, Ridge Regression, Lasso Regression</em>, and <em>Support Vector Regression (SVR)</em>. Regression analysis is one of the most fundamental tools in machine learning and data science, yet improving its robustness and accuracy in noisy, real-world settings remains a persistent challenge; this motivates the incorporation of chaos-inspired features. Our approach was evaluated using ten diverse real-world datasets and a synthetically generated noisy dataset of the form <span><math><mrow><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>c</mi><mo>+</mo><mi>ϵ</mi></mrow></math></span> with various levels of additive Gaussian noise. Results show that incorporating the <em>Tracemean</em> feature (mean of the chaotic neural traces of the neurons in the NL architecture) significantly enhances regression performance, particularly in Augmented Lasso Regression and Augmented SVR, where six out of ten real-life datasets exhibited improved predictive accuracy. Among the models, Augmented Chaotic Ridge Regression achieved the highest average performance (<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>) boost (11.35%). Additionally, experiments on the simulated noisy dataset demonstrated that the Mean Squared Error (MSE) of the augmented models consistently decreased and converged towards the Minimum Mean Squared Error (MMSE) as the sample size increased with various levels of additive Gaussian noise. This work demonstrates the potential of chaos-inspired features in regression tasks, offering a pathway to more accurate, robust and computationally efficient prediction models.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117213"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217921","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":"Fear-driven gregariousness and survival: Modeling bidirectional feedbacks and seasonality in a generalist predator–prey system","authors":"Yalong Xue ,&nbsp;Shengjiang Chen ,&nbsp;Lili Xu ,&nbsp;Fengde Chen","doi":"10.1016/j.chaos.2025.117316","DOIUrl":"10.1016/j.chaos.2025.117316","url":null,"abstract":"<div><div>Prey fear and gregarious behavior form a bidirectional feedback loop critical to ecosystem stability. We quantify this bidirectional feedback by using GSE mechanisms and extending this framework to seasonal environments. Mathematical analysis and numerical simulations validate the proposed model. Research shows that increasing fear intensity eliminates positive equilibria via saddle–node bifurcation, while GSE mitigates this by enhancing group survival. Under bistability, the number, spatial distribution, and stability of interior equilibria exhibit selective dependence on both fear parameter and GSE. Fear and GSE form a feedback loop that can stabilize ecosystems or trigger extinction via bistability. Notably, fear effects and GSE exert opposing influences on model dynamics. Furthermore, it is highlighted that seasonal variations modulate but do not fundamentally alter the underlying stability structure dictated by fear and group size effect. Seasonal forcing amplifies these dynamics, with prey initial density being critical to persistence. This study establishes the first theoretical framework unifying GSE-driven fear feedbacks and seasonal forcing, offering mechanistic insights into ecosystem resilience and extinction thresholds.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117316"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217928","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":"Cooperation dynamics driven by reinforcement learning with interactive diversity in structured populations","authors":"Tianbo An ,&nbsp;Huizhen Zhang ,&nbsp;Zhanshuo Zhang ,&nbsp;Guanghui Liu ,&nbsp;Jiayu Li ,&nbsp;Liangyu Chen ,&nbsp;Zhen Wang","doi":"10.1016/j.chaos.2025.117308","DOIUrl":"10.1016/j.chaos.2025.117308","url":null,"abstract":"<div><div>In reality, individuals tend to make different decisions based on differences in relationships and behaviors with their neighbors. Based on this observation, the paper explores the evolution of cooperative behavior when agents develop separated actions for each neighbor by the reinforcement learning approach. Through simulation experiments, it is shown that our model improves the cooperative level compared to results that only consider the agent’s own behavior. This is because agents tend to adopt cooperative strategies toward their neighbors while avoiding exploitation, thus promoting the steady expansion of cooperation. Notably, we find that agents do not always choose the action with the highest expected rewards. Therefore, we classify the behavior strategies of the agents into 16 types, corresponding to all possible combinations of actions selected in different states. We observe that agents adopting a specific behavior strategy tend to dominate the evolutionary process: when they choose to cooperate, they switch to defection in the next round regardless of the opponent’s action; conversely, when they defect, they switch to cooperation in the next round, again independent of the opponent’s behavior. These agents are typically distributed among others with different strategy types, playing a bridging and buffering role. By facilitating the expansion of neighboring agents, they contribute to the spread of cooperative behavior and ultimately enhance the overall level of cooperation in the population. Similar phenomena are also observed under initial specific distributions (e.g., ALLC, ALLD). Next, the hyperparameters of reinforcement learning are analyzed, and the results show that cooperation is easier to maintain and expand when agents make decisions based on past experiences and fully consider potential future rewards. We also compare this model with a control model that adopted the assumption of interactive homogeneity, and further examine the impact of different network structures on the cooperative evolution. Finally, we introduce the memory mechanism of agents as an extended analysis of the model.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117308"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217927","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":"Experimenting with and analysing reaction–diffusion waves on physicochemical fractal media","authors":"Ivan S. Proskurkin ,&nbsp;Alexandr A. Efimov ,&nbsp;Eugene B. Postnikov ,&nbsp;Dmitry A. Safonov ,&nbsp;Ilya L. Malfanov ,&nbsp;Anastasia I. Lavrova","doi":"10.1016/j.chaos.2025.117299","DOIUrl":"10.1016/j.chaos.2025.117299","url":null,"abstract":"<div><div>We developed a macroscopic physicochemical system based on a thin gel layer (less than 100 <span><math><mi>μ</mi></math></span> m thick) that accurately reproduces the iterative ramification process leading to the Sierpinski gasket, with four self-similar iterations originating from the base triangle. This system, filled with reagents sustaining the Belousov–Zhabotinsky (BZ) reaction in an excitable regime, made it possible to observe and investigate travelling waves propagating through a regular fractal medium—not <em>in silico</em>, but in the physical realm. Video recordings enabled a quantitative assessment of the spatiotemporal dynamics of wave propagation speed for each prefractal, allowing for analysis and comparison of the asymptotic behaviour with predictions derived from mathematical models. Additionally, we discovered and mathematically analysed a novel effect of wave front straightening, which suggests the potential of heterogeneous gel architectures to serve as effective transmitting elements in chemical soft-computing systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117299"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217929","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":"Complex self-organization of mutated soliton supramolecular structures in a passively mode-locked fiber laser","authors":"Yuansheng Ma ,&nbsp;Ziyang Zhang ,&nbsp;Jiangyong He ,&nbsp;Pan Wang ,&nbsp;Hao Zhang ,&nbsp;Zhi Wang ,&nbsp;Yange Liu ,&nbsp;Bo Liu","doi":"10.1016/j.chaos.2025.117311","DOIUrl":"10.1016/j.chaos.2025.117311","url":null,"abstract":"<div><div>Soliton supramolecular structures, as extended entities in the temporal domain, provide a fascinating platform for investigating the nonlinear interactions between solitons. We observed the mutated soliton supramolecular structures in a passively mode-locked fiber laser. Due to the intracavity gain fluctuations and noise perturbations, the distributions of soliton molecules exhibit locally ordered or disordered patterns, yet globally random. Our findings suggest that the generation and annihilation of new solitons or soliton molecules are the primary factors driving the formation of such mutated distributions. These disorders within locally distributions further promote the coexistence of diverse dynamical processes, such as the bound–escape relative motion between the single soliton and soliton molecule, transitions from asynchronous to synchronous states across neighboring systems, and state switching of soliton complexes. Numerical simulations support the formation and evolution mechanisms of these distributions and dynamics within the passive mode-locked dissipative cavity. This research provides new insights into the nonlinear dynamics of mode-locked lasers and has the potential to inspire future applications in nonlinear optical control.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117311"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145217922","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":"Phase transition in lattice hydrodynamic model integrating random anomalous information under connected autonomous vehicles surroundings","authors":"Guanghan Peng ,&nbsp;Yuangui Liu ,&nbsp;Huili Tan ,&nbsp;Dongxue Xia ,&nbsp;Tong Zhou","doi":"10.1016/j.chaos.2025.117274","DOIUrl":"10.1016/j.chaos.2025.117274","url":null,"abstract":"<div><div>As vehicle-to-everything (V2X) communication technology rapidly evolves, connected autonomous vehicles (CAVs) have emerged as a significant component of traffic flow. However, anomalies in the information within the V2X environment can greatly impact the stability of traffic flow composed of CAVs. In this context, we have innovatively constructed a lattice hydrodynamic model by incorporating random anomalous information parameters. This model examines the effect of random anomalous information on the queue of CAVs within the V2X environment, capturing the interference of such information on traffic flow. Furthermore, we conduct linear stability analysis and nonlinear analysis for the new model, successfully deriving the neutral stability conditions and the modified Korteweg-de Vries (mKdV) equation. Additionally, through simulations, we explore the impact of random anomalous information on CAVs from the perspectives of density variation and density differences (limit cycle). Power spectrum and spectral entropy are also applied to investigate traffic stability and complexity under the interference of random anomalous information in the vicinity of CAVs. The simulation results indicate that an increase in the probability of information anomalies significantly degrades the stability of traffic flow, while variations in different anomalous information intensity coefficients produce heterogeneous disturbances in traffic flow dynamics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"201 ","pages":"Article 117274"},"PeriodicalIF":5.6,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218003","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}