Chaos Solitons & Fractals最新文献

{"title":"Analytical and algebraic insights to the generalized Rosenau equation: Lie symmetries and exact solutions","authors":"Ayse Tiryakioglu,&nbsp;Yasin Hasanoglu,&nbsp;Cihangir Ozemir","doi":"10.1016/j.chaos.2025.116263","DOIUrl":"10.1016/j.chaos.2025.116263","url":null,"abstract":"<div><div>In this article we attempted to perform a group-theoretical analysis of a Rosenau equation with a general nonlinearity. We determined certain classes of equations with associated Lie group of transformations and corresponding Lie algebras. For these specific classes, we performed reductions to ordinary differential equations through the optimal system of one-dimensional subalgebras. Further, considering cubic, quintic and cubic–quintic nonlinearities we found some exact solutions of hyperbolic and elliptic type. We also derived Rosenau equations with power-law and exponential type nonlinearities via physical considerations, which well matched with the families of equations suggested by the Lie symmetry classification.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116263"},"PeriodicalIF":5.3,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629229","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":"Complete synchronization in predetermined/fixed-time for multilayered networks under edge-based discontinuous control","authors":"Tingting Zhao ,&nbsp;Yu Zhou ,&nbsp;Yiwen Qi ,&nbsp;Jie Huang","doi":"10.1016/j.chaos.2025.116270","DOIUrl":"10.1016/j.chaos.2025.116270","url":null,"abstract":"<div><div>Achieving synchronization in a designated time for multilayered networks (MLNs) is particularly challenging when state information is unavailable. This study provides theoretical solutions to the fixed-time (FIM) and predetermined-time (PIM) synchronization problems in MLNs. Firstly, a high-resolution model of MLNs is established with both intra-layer and inter-layer coupling. Additionally, a practical PIM stability theorem and high-precision settling time estimation are formulated. Furthermore, two edge-based event-triggered intermittent control (EAIC) strategies are developed for MLNs using various auxiliary functions. FIM/PIM synchronization issues are addressed while eliminating Zeno behaviors throughout, except during the settling time. Ultimately, the feasibility of the proposed theory is demonstrated through the design of a synchronization circuit within the complex system.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116270"},"PeriodicalIF":5.3,"publicationDate":"2025-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636456","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":"Higher-order soliton, rogue wave and breather solutions of a generalized Fokas–Lenells equation","authors":"Jiao Wei ,&nbsp;Jiajia Li ,&nbsp;Minxin Jia ,&nbsp;Xin Wang","doi":"10.1016/j.chaos.2025.116252","DOIUrl":"10.1016/j.chaos.2025.116252","url":null,"abstract":"<div><div>Under investigation is a generalized Fokas–Lenells equation, which is the first nontrivial equation in the negative hierarchy flow associated with a 2 × 2 matrix spectral problem involving two potentials. Based on the <span><math><mi>N</mi></math></span>-fold classical Darboux transformation, the (<span><math><mi>n</mi></math></span>, <span><math><mi>N</mi></math></span>-<span><math><mi>n</mi></math></span>)-fold generalized Darboux transformation is constructed by means of the limit technique. As an application, the higher-order localized wave solution in a compact determinant form with arbitrary order is derived for the generalized Fokas–Lenells equation. The bright-dark soliton solutions from first to third order under a zero background are obtained. Specifically, unlike the bright rogue wave and breather solutions of the standard Fokas–Lenells equation, the bright-dark and bright-bright rogue wave solutions as well as breather solutions from first to third order under a nonzero background of the generalized Fokas–Lenells equation are presented. Furthermore, the hybrid rogue wave-breather solutions from second to third order are given. The dynamical behaviors of these explicit solutions are all displayed graphically.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116252"},"PeriodicalIF":5.3,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629952","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":"Backstepping control for stochastic strict-feedback systems with Lévy noise","authors":"K. Mathiyalagan,&nbsp;T. Elizabeth Jeyanthi","doi":"10.1016/j.chaos.2025.116241","DOIUrl":"10.1016/j.chaos.2025.116241","url":null,"abstract":"<div><div>In this paper, a class of nonlinear strict-feedback continuous time stochastic jump diffusion system (SJDS) driven by Lévy noise is considered. The aim of this work is to design control function for the system to obtain global asymptotic stability at the origin in probability. Backstepping method is used to design the robust stabilizing control function. Also, quartic form Lyapunov functional is utilized to stabilize the system with high amplified energy. Fourth-moment exponential stability conditions for the closed loop system are derived using It<span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>’s differential. Further, numerical examples are presented to show the applications of the theoretical results to physical systems. The effectiveness of the designed control function in the process of convergence of error vector are depicted in the form of error covariance matrices in the simulation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116241"},"PeriodicalIF":5.3,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629949","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":"Analyzing unsteady flow of shear-thinning nanofluids over a cylinder with exponential stretching and shrinking: An artificial neural network approach","authors":"Saeed Ehsan Awan ,&nbsp;Fazal Badshah ,&nbsp;Muhammad Awais ,&nbsp;Nabeela Parveen ,&nbsp;Zulqurnain Sabir ,&nbsp;Zuhaib Ashfaq Khan","doi":"10.1016/j.chaos.2025.116301","DOIUrl":"10.1016/j.chaos.2025.116301","url":null,"abstract":"<div><div>Current study aims to implement a novel intelligent numerical computing framework by applying a computational artificial neural network designated with Bayesian regularization network (BRN) to underscore a comparative analysis for the impact of unsteady shear-thinning behavior of the flow of nanofluid through an exponentially stretching or shrinking cylinder. Transformed governing model of ordinary differential equations in cylindrical coordinates based on Buongiorno model is analyzed. The reference dataset for Buongiorno model is obtained by using Adam numerical solver against six scenarios with the variation of parameters namely, stretching/shrinking parameter, Weissenberg number, Reynold number, Brownian motion parameter, Prandtl number, and Lewis number. The acquired datasets are feed into a supervised computational framework utilizing BRN to approximate solutions for the unsteady shear-thinning behavior of flow system. The robustness of the stochastic process based on the BRN is validated through extensive simulation including convergence plots using the mean square errors, the performance of adaptive control parameters in the optimization algorithm, error distribution histograms and regression analysis. The optimal validation performance is observed in relation to epoch number index at epoch 621, 239, 548, 427, 580, 826 and 717 respective to all the scenarios. Further, observed mean squared errors (MSE) between target and output data of approximately 1.1383 × 10⁻¹¹, 4.4409 × 10⁻¹¹, 4.3824 × 10⁻¹², 3.7145 × 10⁻¹², 3.4385 × 10⁻¹³, 1.0341 × 10⁻¹¹and 3.1188 × 10⁻¹¹, recorded at times of 2 s, 1 s, 2 s, 2 s, 3 s, and 2 s respectively. These quantitative measures demonstrate minimal error margin which ensure the reliable alignment with numerical data.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116301"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629950","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 metrological performance of WW¯-like state in Ising model","authors":"Yan Li ,&nbsp;Zhihong Ren","doi":"10.1016/j.chaos.2025.116257","DOIUrl":"10.1016/j.chaos.2025.116257","url":null,"abstract":"<div><div>We examine the metrological performance of <span><math><mrow><mi>W</mi><mover><mrow><mi>W</mi></mrow><mo>¯</mo></mover></mrow></math></span>-like state (<span><math><mrow><mi>α</mi><msub><mrow><mfenced><mrow><mi>W</mi></mrow></mfenced></mrow><mrow><mi>N</mi></mrow></msub><mo>+</mo><mi>β</mi><msub><mrow><mfenced><mrow><mover><mrow><mi>W</mi></mrow><mo>¯</mo></mover></mrow></mfenced></mrow><mrow><mi>N</mi></mrow></msub></mrow></math></span>) in quantum phase estimation. Based on the framework of quantum interferometry, we analytically derive the quantum Fisher information (QFI) and analyze the precision limits. In the noninteracting environment, the metrological power of <span><math><mrow><mi>W</mi><mover><mrow><mi>W</mi></mrow><mo>¯</mo></mover></mrow></math></span>-like state is same as that of the <span><math><mi>W</mi></math></span> state in few-qubit case but symmetrically enhanced (with respect to <span><math><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>) in large-qubit case. In the Ising model, with increasing interaction strength, the QFI of <span><math><mrow><mi>N</mi><mo>≤</mo><mn>6</mn></mrow></math></span> qubit <span><math><mrow><mi>W</mi><mover><mrow><mi>W</mi></mrow><mo>¯</mo></mover></mrow></math></span>-like state is universally enhanced and displays different and exotic trends (with respect to <span><math><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>), particularly for 4- and 6-qubit cases where it respectively shows a reversible phenomenon and a reversal scenario. Regarding others (<span><math><mrow><mi>N</mi><mo>&gt;</mo><mn>6</mn></mrow></math></span>), it exhibits a similar trend that the precision limit is always better than that of <span><math><mrow><mi>W</mi><mover><mrow><mi>W</mi></mrow><mo>¯</mo></mover></mrow></math></span> state in strong interaction.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116257"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618232","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":"Correction note to: Yoshioka, H. (2025). Superposition of interacting stochastic processes with memory and its application to migrating fish counts. Chaos, Solitons & Fractals. Vol. 192, 115911","authors":"Hidekazu Yoshioka","doi":"10.1016/j.chaos.2025.116264","DOIUrl":"10.1016/j.chaos.2025.116264","url":null,"abstract":"<div><div>This is a correction note to Proposition 3 in the following paper (called Y25 in this letter): <strong>Yoshioka H. (2025). Superposition of interacting stochastic processes with memory and its application to migrating fish counts. Chaos, Solitons &amp; Fractals. Vol. 192, 115911. doi:</strong><span><span>https://doi.org/10.1016/j.chaos.2024.115911</span><svg><path></path></svg></span><strong>.</strong></div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116264"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618263","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":"Deterministic and stochastic dynamic analysis of a Parkinson’s disease model","authors":"Yuanhong Bi ,&nbsp;Xiaoqi Zhang ,&nbsp;Quansheng Liu","doi":"10.1016/j.chaos.2025.116207","DOIUrl":"10.1016/j.chaos.2025.116207","url":null,"abstract":"<div><div>Parkinson’s disease (PD) is closely related to high level of reactive oxygen species (ROS) and misfolded <span><math><mi>α</mi></math></span>-synaptic protein (<span><math><msup><mrow><mi>α</mi><mtext>SYN</mtext></mrow><mrow><mo>∗</mo></mrow></msup></math></span>). A deterministic model of ROS and <span><math><msup><mrow><mi>α</mi><mtext>SYN</mtext></mrow><mrow><mo>∗</mo></mrow></msup></math></span> was proposed by Cloutier et al, who analyzed the effect of different stress signals on a switch from low level to high one for ROS. In this paper, we further investigate the existence and stability of a positive equilibrium of the deterministic model and derive the conditions on which the model experiences saddle–node bifurcation inducing a bistability with low and high levels. Then, a stochastic model of ROS and <span><math><msup><mrow><mi>α</mi><mtext>SYN</mtext></mrow><mrow><mo>∗</mo></mrow></msup></math></span> is formulated through considering Gaussian white noise into the deterministic one. The existence of global unique positive solution is analyzed and sufficient conditions for the existence of stationary distribution are provided for the stochastic model. Furthermore, noise-induced transition between the bistability is explored through confidence ellipse for the same noise intensity and the average number of alternations between the bistability and the average dominance duration that the model spends on a stable steady state for different noise intensity. Our results reveal that ROS displays bistability with low and high levels under moderate stress. In the presence of noise, the decreasing of stress and the increasing of noise intensity easily induce the transition from high stable steady state to low one to relieve the disease. In addition, smaller stress is an important factor in suppressing the transition from low stable steady state to high one, which also can be prevented by decreasing noise intensity for larger stress. Therefore, disease state can switch to healthy state through regulating noise intensity. Our results may provide a new idea to control noise to alleviate PD through physical therapy.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116207"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619793","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 volatility model with long memory for water quantity-quality dynamics","authors":"Hidekazu Yoshioka ,&nbsp;Yumi Yoshioka","doi":"10.1016/j.chaos.2025.116167","DOIUrl":"10.1016/j.chaos.2025.116167","url":null,"abstract":"<div><div>Water quantity and quality are vital indices for assessing fluvial environments. These indices are highly variable over time and include sub-exponential memory, where the influences of past events persist over long durations. Moreover, water quantity and quality are interdependent, with the former affecting the latter. However, this relationship has not been thoroughly studied from the perspective of long-memory processes, which this paper aims to address. We propose applying a new stochastic volatility model, a system of infinite-dimensional stochastic differential equations, to describe dynamic asset prices in finance and economics. Although the stochastic volatility model was originally developed for phenomena unrelated to the water environment, its mathematical universality allows for an interdisciplinary reinterpretation: river discharge is analogous to volatility, and water quality to asset prices. Moreover, the model's infinite-dimensional nature enables the analytical description of sub-exponential memory. The moments and autocorrelations of the model are then obtained analytically. We mathematically analyze the stochastic volatility model and investigate its applicability to the dynamics of water quantity and quality. Finally, we apply the model to real time-series data from a river in Japan, demonstrating that it effectively captures both the memory and the correlation of water quality indices to river discharge. This approach, grounded in infinite-dimensional stochastic differential equations, represents a novel contribution to the modeling and analysis of environmental systems where long memory processes play a role.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116167"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629951","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":"Second-order locally active memristor based neuronal circuit","authors":"Yidan Mao,&nbsp;Yujiao Dong,&nbsp;Zhenzhou Lu,&nbsp;Chenyang Xiang,&nbsp;Jinqi Wang,&nbsp;Yan Liang","doi":"10.1016/j.chaos.2025.116279","DOIUrl":"10.1016/j.chaos.2025.116279","url":null,"abstract":"<div><div>Brain-like neurons inspired by biology are critical in constructing neuromorphic computing architectures with high energy efficiency. Memristors, characterized by their nanoscale and nonlinearity, have emerged as prime candidates for realizing artificial neuron. Considering the integration density, we propose a voltage-controlled locally active memristor (LAM) with second-order complexity. In contrast to first-order memristors, the locally active domains (LADs) of the second-order memristor cannot be determined solely by the DC <em>V</em>–<em>I</em> curve, then the small-signal method is introduced to identify all LADs, which are classified as Class I and Class II. Based on the capacitive or inductive characteristics of the memristor operating at different locally active voltages judged by its frequency response, a simple third-order neuronal circuit that incorporates compensate components such as an inductor or a capacitor can be built. Further exploration on the edge of chaos relying on the admittance function measures the type and value of the compensate component. We take the operating points with capacitive features as an example, which require an inductive device in series with the memristor and a biasing voltage source. The built neuronal circuit replicates twelve brain-like behaviors, especially class I and class II excitability, all-or-nothing firing, and refractory period, whose generation mechanism is investigated via the dynamic map, Lyapunov exponents, and bifurcation plot. The circuit simulation results also demonstrate the effectiveness of theoretical analyses on the second-order memristor and the third-order memristive neuron.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116279"},"PeriodicalIF":5.3,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143618228","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}