IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0288919

Caleb Monoran, Clifford Watkins, Sean Breckling

引用次数: 0

The nonlinear Fokker-Planck equation with nongradient drift forces and an anisotropic potential. 具有非梯度漂移力和各向异性势的非线性Fokker-Planck方程。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0280921

V T F de Luca, R S Wedemann, A R Plastino

{"title":"The nonlinear Fokker-Planck equation with nongradient drift forces and an anisotropic potential.","authors":"V T F de Luca, R S Wedemann, A R Plastino","doi":"10.1063/5.0280921","DOIUrl":"https://doi.org/10.1063/5.0280921","url":null,"abstract":"Studies regarding physical phenomena described by nonlinear Fokker-Planck equations usually consider the case where the drift forces acting on the physical system under investigation are derived from the gradient of a potential function. In the present manuscript, we investigate nonlinear Fokker-Planck equations, where the drift field has a component that is derived from the gradient of an asymmetric potential and another that corresponds to a nongradient force term. We consider the specific case of a two-dimensional, nonlinear Fokker-Planck equation where the drift field is obtained from an anisotropic, harmonic potential, besides the nongradient term. We analyze the conditions under which this evolution equation admits stationary solutions that are q-exponentials. We prove that this equation admits q-Gaussian, time-dependent solutions that evolve to stationary forms and discuss some of their important properties. Interpreting the evolving probability densities as describing an ensemble of particles, we derived and numerically studied the concomitant trajectories. The theoretical framework discussed in the present contribution enlarges substantially the range of possible applications of the Sq-based, nonlinear Fokker-Planck formalism to the study of problems in diverse types of complex systems in physics, biology, economics, artificial neural networks, and other areas. Importantly, it allows us to approach the problem of modeling systems where the interaction among elements are not symmetrical, as is the case, for example, in neural networks of the brain.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144999780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Structural sensitivity of a tri-trophic food chain model in a parameter plane. 三营养食物链模型在参数平面上的结构敏感性。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0275113

Ruma Kumbhakar, Saheb Pal, Nikhil Pal

{"title":"Structural sensitivity of a tri-trophic food chain model in a parameter plane.","authors":"Ruma Kumbhakar, Saheb Pal, Nikhil Pal","doi":"10.1063/5.0275113","DOIUrl":"https://doi.org/10.1063/5.0275113","url":null,"abstract":"Biological models are important in describing species interaction, disease spread, and environmental processes. One key aspect in improving the predictive capability of these models is deciding which parametrization is used to formulate the mathematical model. Considering two distinct functions with similar shapes and the same qualitative properties in a model can lead to markedly different model predictions. Such a phenomenon is recognized as the structural sensitivity of models. In this article, we investigate the structural sensitivity of a tri-trophic food chain model in a parameter plane by considering three nearly indistinguishable forms of the trophic function, namely, Holling type-II, Ivlev, and trigonometric. We use various tools, including bifurcation diagrams, isospike diagrams, and Lyapunov exponent diagrams, to explore the structural sensitivity of the model. The findings show that a functional form has a significant impact on the organization of periodic structures in the parameter plane. The model exhibits a range of diverse dynamics in a fixed parameter range with variations in the functional form. The survival of species and the nature of oscillations are heavily influenced by the model's constituent functions. Our results suggest that even slight variations in the functional response curves can lead to significant differences in the qualitative and quantitative dynamics of a food chain model.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Chaos aided regime of laser/electromagnetic energy absorption by plasma. 等离子体激光/电磁能量吸收的混沌辅助状态。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0271910

Rohit Juneja, Amita Das, Trishul Dhalia, Animesh Sharma

{"title":"Chaos aided regime of laser/electromagnetic energy absorption by plasma.","authors":"Rohit Juneja, Amita Das, Trishul Dhalia, Animesh Sharma","doi":"10.1063/5.0271910","DOIUrl":"https://doi.org/10.1063/5.0271910","url":null,"abstract":"The absorption of laser energy by plasma is of paramount importance for various applications. Collisional and resonant processes are often invoked for this purpose. However, in some contexts (e.g., in vacuum [Brunel, Phys. Rev. Lett. 59, 52 (1987)] and the J→×B→ heating [Kruer and Estabrook, Phys. Fluids 28, 430-432 (1985)]), the energy transfer occurs even when plasma is collisionless, and there is no resonant process involved. The energy absorption in these cases has been attributed to the sheath electrostatic fields that get generated as the electrons are pulled out in the vacuum from the plasma medium. The origin of irreversibility aiding the absorption, in these cases, remains to be understood. Particle-in-Cell simulations using the OSIRIS 4.0 platform have been carried out. The nearby trajectories of lighter electron species involved in the interaction with the laser show exponential separation. This is confirmed by the positive Lyapunov index, as well as by phase space reconstruction and correlation dimension analysis. The observations in these cases are contrasted with the electron cyclotron resonant case, which shows negligible chaos in the electron trajectories despite the energy absorption percentage being high.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145014020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Predicting copper recovery from flotation using machine learning and laboratory-generated data. 利用机器学习和实验室生成的数据预测浮选中铜的回收率。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0278193

José Benítez, Víctor Flores, Sergio Curilef, Rafael Martínez-Pelaez, Claudio Leiva

{"title":"Predicting copper recovery from flotation using machine learning and laboratory-generated data.","authors":"José Benítez, Víctor Flores, Sergio Curilef, Rafael Martínez-Pelaez, Claudio Leiva","doi":"10.1063/5.0278193","DOIUrl":"https://doi.org/10.1063/5.0278193","url":null,"abstract":"The efficient extraction of copper is becoming increasingly complex due to the declining availability of high-grade ore deposits and the implementation of more rigorous environmental standards. These constraints have heightened the demand for advanced technologies that optimize copper recovery through processes, such as flotation. Flotation, a widely employed physicochemical separation technique, is highly sensitive to operational parameters, making its optimization essential for maximizing metal recovery, reducing operational costs, and promoting environmentally responsible resource utilization and conservation. This study investigates applying Machine Learning (ML) techniques to improve flotation process performance. Specifically, this study assesses the predictive performance of four ML algorithms: random forest, support vector machine, K-means clustering, and Artificial Neural Networks (ANNs) for estimating copper recovery in flotation processes. The models were trained and validated using experimental data from a laboratory-scale flotation system. Among the evaluated algorithms, the ANN achieved the highest prediction accuracy of 98.69%, demonstrating a strong capacity to model complex nonlinear interactions among critical process variables. Complementary, disequilibrium, and entropic measures validate the results using the probability selection between three classes. These results highlight the potential of ML-based approaches to support process optimization, enhance recovery efficiency, and contribute to the sustainable development of copper extraction technologies.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145039231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractal geometry predicts dynamic differences in structural and functional connectomes. 分形几何预测结构和功能连接体的动态差异。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0283805

Anca Rădulescu, Eva Kaslik, Alexandru Fikl, Johan Nakuci, Sarah Muldoon, Michael Anderson

{"title":"Fractal geometry predicts dynamic differences in structural and functional connectomes.","authors":"Anca Rădulescu, Eva Kaslik, Alexandru Fikl, Johan Nakuci, Sarah Muldoon, Michael Anderson","doi":"10.1063/5.0283805","DOIUrl":"https://doi.org/10.1063/5.0283805","url":null,"abstract":"Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely used to characterize these networks, they often fail to fully capture the emergent properties of large-scale neural dynamics. Here, we introduce an alternative approach to quantify brain networks that is rooted in complex dynamics, fractal geometry, and asymptotic analysis. We apply these concepts to brain connectomes and demonstrate how quadratic iterations and geometric properties of Mandelbrot-like sets can provide novel insights into structural and functional network dynamics. Our findings reveal fundamental distinctions between structural (positive) and functional (signed) connectomes, such as the shift of cusp orientation and the variability in equi-M set geometry. Notably, structural connectomes exhibit more robust, predictable features, while functional connectomes show increased variability for non-trivial tasks. We further demonstrate that traditional graph-theoretical measures, when applied separately to the positive and negative sub-networks of functional connectomes, fail to fully capture their dynamic complexity. Instead, size and shape-based invariants of the equi-M set effectively differentiate between rest and emotional task states, which highlights their potential as superior markers of emergent network dynamics. These results suggest that incorporating fractal-based methods into network neuroscience provides a powerful tool for understanding how information flows in natural systems beyond static connectivity measures, while maintaining simplicity.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145136568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Arnold tongues replace period-doubling cascades in a memristor circuit. 阿诺德舌取代了忆阻电路中的倍周期级联。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0277414

Silvio L T de Souza, Antonio M Batista, Iberê L Caldas

引用次数: 0

Traffic flow-oriented reliability assessment and enhancement of urban transportation networks. 面向交通流的城市交通网络可靠性评估与提升。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0277379

Yihong Bao, Qihang Chen, Dingding Han

{"title":"Traffic flow-oriented reliability assessment and enhancement of urban transportation networks.","authors":"Yihong Bao, Qihang Chen, Dingding Han","doi":"10.1063/5.0277379","DOIUrl":"https://doi.org/10.1063/5.0277379","url":null,"abstract":"System reliability is a critical aspect of urban transport networks. It ensures that modern cities can provide safe, efficient, and resilient mobility services. However, existing reliability studies primarily focus on network topology and connectivity, overlooking the impact of disruptions on passenger travel quality and the temporal heterogeneity inherent in traffic patterns. Here, we propose a traffic flow-oriented reliability analysis method. This method integrates real-world passenger flow data into a percolation-based reliability evaluation. Specifically, we construct a weighted network model that accounts for commuting time costs and transfer penalties. We also introduce traffic-aware centralities to identify critical links and propose reliability metrics that consider both traffic flow preservation and travel time variation in the event of disruptions. We further evaluate two protection strategies to enhance system reliability. We apply our approach to the Shanghai metro system and conduct extensive numerical simulations across different traffic patterns. Our results show that failing to consider travel quality can lead to an underestimation of network vulnerability. We also demonstrate that a centrality-based protection strategy improves the effectiveness and repeatability of protected links under similar traffic patterns. This study offers a data-driven, temporally adaptive methodology for evaluating and enhancing the reliability of urban transportation systems, providing insights for infrastructure planning and risk management in smart cities.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144991589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tailored minimal reservoir computing: On the bidirectional connection between nonlinearities in the model and in data. 定制最小油藏计算：关于模型非线性与数据非线性之间的双向联系。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0272793

Davide Prosperino, Haochun Ma, Christoph Räth

{"title":"Tailored minimal reservoir computing: On the bidirectional connection between nonlinearities in the model and in data.","authors":"Davide Prosperino, Haochun Ma, Christoph Räth","doi":"10.1063/5.0272793","DOIUrl":"https://doi.org/10.1063/5.0272793","url":null,"abstract":"We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers (RCs), focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable nonlinearity parameter, we explore how the predictive performance varies with the degree of nonlinearity in the model. To provide controlled testbeds, we generalize to the fractional Halvorsen system, a novel chaotic system with fractional exponents. Our experiments reveal that the prediction performance is maximized when the model's nonlinearity matches the nonlinearity present in the data. In cases where multiple nonlinearities are present in the data, we find that the correlation dimension of the predicted signal is reconstructed correctly when the smallest nonlinearity is matched. We use this observation to propose a method for estimating the minimal nonlinearity in unknown time series, by sweeping the model exponent and identifying the transition to a successful reconstruction. Applying this method to both synthetic and real-world datasets, including financial time series, we demonstrate its practical viability. Additionally, we briefly study the SINDy framework as a complementary approach for identifying nonlinearities in data. Finally, we transfer these insights to classical RCs, by augmenting traditional architectures with fractional, generalized reservoir states. This yields performance gains, particularly in resource-constrained scenarios, such as physical reservoirs, where increasing reservoir size is impractical or economically unviable. Our work provides a principled route toward tailoring RCs to the intrinsic complexity of the systems they aim to model.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144991647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Homotopy reservoir computing: Harnessing chaos for computation. 同伦油藏计算：利用混沌进行计算。

IF 3.2 2区数学

Chaos Pub Date : 2025-09-01 DOI: 10.1063/5.0273406

Jaesung Choi, Pilwon Kim

引用次数: 0

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