Pub Date : 2025-02-22DOI: 10.1016/j.chaos.2025.116150
Marzena Ciszak , Francesco Marino
Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the transition between these two regimes, where the dynamics consists of periods of nearly regular bursting interspersed with irregular spiking intervals, and demonstrate its correspondence to intermittent transition to chaos. Specifically, we consider a bimodal Kuramoto model with linear global feedback, which allows for a mean-field formulation of the dynamics and thus to investigate the phenomenology in the thermodynamic limit. We reconstruct the one-dimensional first-return maps of inter-burst intervals and estimate the Floquet multiplier associated with the unstable bursting solution. The results indicate type-III intermittency, which is also supported by the scaling of the average laminar periods as the control parameter varies, along with their probability density distribution.
{"title":"Type-III intermittency in emergent bursting dynamics of globally coupled rotators","authors":"Marzena Ciszak , Francesco Marino","doi":"10.1016/j.chaos.2025.116150","DOIUrl":"10.1016/j.chaos.2025.116150","url":null,"abstract":"<div><div>Globally coupled populations of phase rotators with linear adaptive coupling can exhibit collective bursting oscillations between asynchronous and partially synchronized states, which can be either periodic or chaotic. Here, we analyze the transition between these two regimes, where the dynamics consists of periods of nearly regular bursting interspersed with irregular spiking intervals, and demonstrate its correspondence to intermittent transition to chaos. Specifically, we consider a bimodal Kuramoto model with linear global feedback, which allows for a mean-field formulation of the dynamics and thus to investigate the phenomenology in the thermodynamic limit. We reconstruct the one-dimensional first-return maps of inter-burst intervals and estimate the Floquet multiplier associated with the unstable bursting solution. The results indicate type-III intermittency, which is also supported by the scaling of the average laminar periods as the control parameter varies, along with their probability density distribution.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116150"},"PeriodicalIF":5.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-22DOI: 10.1016/j.chaos.2025.116147
Sapavat Bixapathi, A. Benerji Babu
This study aims to investigates the influence of internal heat and chemical reactions, combined with vertical magnetic field modulation, on the nonlinear magneto-convection of a Jeffrey fluid in a horizontally porous layer subjected to differential heating. The problem is critical for understanding stability in porous systems under combined thermal, magnetic, and reactive effects, relevant to energy storage, geophysics, and industrial processes. Linear stability analysis is employed, solving the generalized eigenvalue problem using the Galerkin technique to determine the critical thermal Rayleigh number for a wide range of parameters. Results reveal that increased magnetic field strength () raises , significantly delaying convection onset. A weakly nonlinear stability analysis is conducted to explore the system’s nonlinear behavior. Expanding small-axisymmetric disturbances in a power series of convection amplitude leads to deriving a nonautonomous nonlinear cubic Ginzburg–Landau equation. Numerical solutions of this equation yield the Nusselt and Sherwood numbers as functions of key parameters. The results demonstrate that increases in the Jeffrey fluid parameter, modulation frequency, magnetic field, and Darcy number lead to reductions in both heat and mass transfer, thereby enhancing system stability. The findings highlight the stabilizing role of magnetic field modulation and the interplay between fluid and porous medium properties, providing novel insights into controlling convection in magneto-reactive systems. This work extends previous efforts by incorporating non-linear magnetic field modulation effects and elucidating their quantitative impact on heat and mass transfer metrics, revealing critical nonlinear dynamics with implications for astrophysical phenomena such as heat transport in stellar interiors and planetary systems.
{"title":"Influence of internal heat and chemical reaction on magneto-convection in a Jeffrey fluid under magnetic field modulation","authors":"Sapavat Bixapathi, A. Benerji Babu","doi":"10.1016/j.chaos.2025.116147","DOIUrl":"10.1016/j.chaos.2025.116147","url":null,"abstract":"<div><div>This study aims to investigates the influence of internal heat and chemical reactions, combined with vertical magnetic field modulation, on the nonlinear magneto-convection of a Jeffrey fluid in a horizontally porous layer subjected to differential heating. The problem is critical for understanding stability in porous systems under combined thermal, magnetic, and reactive effects, relevant to energy storage, geophysics, and industrial processes. Linear stability analysis is employed, solving the generalized eigenvalue problem using the Galerkin technique to determine the critical thermal Rayleigh number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>T</mi><mi>c</mi></mrow></msub></math></span> for a wide range of parameters. Results reveal that increased magnetic field strength (<span><math><mi>Q</mi></math></span>) raises <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>T</mi><mi>c</mi></mrow></msub></math></span>, significantly delaying convection onset. A weakly nonlinear stability analysis is conducted to explore the system’s nonlinear behavior. Expanding small-axisymmetric disturbances in a power series of convection amplitude leads to deriving a nonautonomous nonlinear cubic Ginzburg–Landau equation. Numerical solutions of this equation yield the Nusselt and Sherwood numbers as functions of key parameters. The results demonstrate that increases in the Jeffrey fluid parameter, modulation frequency, magnetic field, and Darcy number lead to reductions in both heat and mass transfer, thereby enhancing system stability. The findings highlight the stabilizing role of magnetic field modulation and the interplay between fluid and porous medium properties, providing novel insights into controlling convection in magneto-reactive systems. This work extends previous efforts by incorporating non-linear magnetic field modulation effects and elucidating their quantitative impact on heat and mass transfer metrics, revealing critical nonlinear dynamics with implications for astrophysical phenomena such as heat transport in stellar interiors and planetary systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116147"},"PeriodicalIF":5.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463933","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}
Pub Date : 2025-02-22DOI: 10.1016/j.chaos.2025.116162
Li Zhang, Wuyin Jin
To reproduce the process of muscle fibers responding to electrical impulses and executing actions, a photosensitive neural circuit is designed to actuate a moving beam, translating ambient light signals into biological responses and movement processes. The mode selection and action mechanism of light signals on the moving beam are elucidated through dynamic analysis and the evolution of Hamilton energy. Activation of the neuron under single stimulus leads various oscillation modes in the beam, including bursting, spiking, and quasi-periodic oscillations. The beam preferentially responds to stimuli inducing quasi-periodic oscillation when dual stimuli are applied. And the beams are more sensitive to stimuli evoking spiking oscillation in the coupled system connected via electrical synapse. These results indicate synergistic and competitive effects of multiple stimuli in muscle movement, providing guidance for the design of intelligent prostheses that flexibly respond to different tasks and adapt to environmental changes.
{"title":"Selective response of artificial muscles to multiple stimuli under neural circuit control","authors":"Li Zhang, Wuyin Jin","doi":"10.1016/j.chaos.2025.116162","DOIUrl":"10.1016/j.chaos.2025.116162","url":null,"abstract":"<div><div>To reproduce the process of muscle fibers responding to electrical impulses and executing actions, a photosensitive neural circuit is designed to actuate a moving beam, translating ambient light signals into biological responses and movement processes. The mode selection and action mechanism of light signals on the moving beam are elucidated through dynamic analysis and the evolution of Hamilton energy. Activation of the neuron under single stimulus leads various oscillation modes in the beam, including bursting, spiking, and quasi-periodic oscillations. The beam preferentially responds to stimuli inducing quasi-periodic oscillation when dual stimuli are applied. And the beams are more sensitive to stimuli evoking spiking oscillation in the coupled system connected via electrical synapse. These results indicate synergistic and competitive effects of multiple stimuli in muscle movement, providing guidance for the design of intelligent prostheses that flexibly respond to different tasks and adapt to environmental changes.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116162"},"PeriodicalIF":5.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463801","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}
Pub Date : 2025-02-21DOI: 10.1016/j.chaos.2025.116114
Robert Benassai-Dalmau, Javier Borge-Holthoefer, Albert Solé-Ribalta
Understanding and characterizing pedestrian mobility is essential for designing more sustainable urban environments. While many studies have examined pedestrian mobility and navigation from diverse perspectives, the analysis of how geospatial features and city organization facilitate or hinder pedestrian movement has been relatively limited. This gap underscores the need for theoretical and analytical approaches. To this end, we explore pedestrian mobility through the lens of discrete vector fields, leveraging random walk models to analyze the impact of sidewalk network structures on pedestrian dynamics. The comparison of discrete-time and continuous-time random walks confirms that the latter provides a suitable framework, as it allows to incorporates edge lengths and pedestrian speeds. Findings highlight that areas with shorter edge links and more intricate network structures exhibit higher pedestrian permeability, supporting urban theories on walkability and accessibility, as described by Jacobs. These results cannot be directly obtained with discrete-time random walks. Testing on sidewalk networks from Barcelona, Paris, and Boston demonstrates how local geometric features and street layouts shape pedestrian permeability. This framework offers a novel quantitative approach to urban mobility, reinforcing theoretical perspectives on urban permeability and providing insights for fostering pedestrian-friendly city designs.
{"title":"Exploring pedestrian permeability in urban sidewalk networks","authors":"Robert Benassai-Dalmau, Javier Borge-Holthoefer, Albert Solé-Ribalta","doi":"10.1016/j.chaos.2025.116114","DOIUrl":"10.1016/j.chaos.2025.116114","url":null,"abstract":"<div><div>Understanding and characterizing pedestrian mobility is essential for designing more sustainable urban environments. While many studies have examined pedestrian mobility and navigation from diverse perspectives, the analysis of how geospatial features and city organization facilitate or hinder pedestrian movement has been relatively limited. This gap underscores the need for theoretical and analytical approaches. To this end, we explore pedestrian mobility through the lens of discrete vector fields, leveraging random walk models to analyze the impact of sidewalk network structures on pedestrian dynamics. The comparison of discrete-time and continuous-time random walks confirms that the latter provides a suitable framework, as it allows to incorporates edge lengths and pedestrian speeds. Findings highlight that areas with shorter edge links and more intricate network structures exhibit higher pedestrian permeability, supporting urban theories on walkability and accessibility, as described by Jacobs. These results cannot be directly obtained with discrete-time random walks. Testing on sidewalk networks from Barcelona, Paris, and Boston demonstrates how local geometric features and street layouts shape pedestrian permeability. This framework offers a novel quantitative approach to urban mobility, reinforcing theoretical perspectives on urban permeability and providing insights for fostering pedestrian-friendly city designs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116114"},"PeriodicalIF":5.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, a fixed-time distributed tracking control problem for unknown nonlinear multi-agent systems (MASs) is investigated. Unlike the existing works on quantized control for MASs, the input signals and states of each agent are communicated via directed networks and quantized before communication. The incorporation of quantized states into the virtual controllers results in their discontinuity, thereby rendering traditional backstepping technique inapplicable. To address this problem, the following steps are proposed: firstly, auxiliary intermediate controllers are designed using unquantized states. Secondly, by replacing the unquantized states with quantized states in the auxiliary intermediate controllers, both the intermediate controllers and the actual controller are obtained. Thirdly, to compensate for the impact of quantization errors, Lemma 10 is introduced. Furthermore, a new distributed adaptive fixed-time consensus (FTC) control strategy is established and the fixed-time stability of system is analyzed.
{"title":"Fixed-time neural consensus control for nonlinear multiagent systems with state and input quantization","authors":"Wenjing Cheng , Huidong Cheng , Fang Wang , Xueyi Zhang","doi":"10.1016/j.chaos.2025.116145","DOIUrl":"10.1016/j.chaos.2025.116145","url":null,"abstract":"<div><div>In this article, a fixed-time distributed tracking control problem for unknown nonlinear multi-agent systems (MASs) is investigated. Unlike the existing works on quantized control for MASs, the input signals and states of each agent are communicated via directed networks and quantized before communication. The incorporation of quantized states into the virtual controllers results in their discontinuity, thereby rendering traditional backstepping technique inapplicable. To address this problem, the following steps are proposed: firstly, auxiliary intermediate controllers are designed using unquantized states. Secondly, by replacing the unquantized states with quantized states in the auxiliary intermediate controllers, both the intermediate controllers and the actual controller are obtained. Thirdly, to compensate for the impact of quantization errors, Lemma 10 is introduced. Furthermore, a new distributed adaptive fixed-time consensus (FTC) control strategy is established and the fixed-time stability of system is analyzed.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116145"},"PeriodicalIF":5.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454712","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}
Pub Date : 2025-02-21DOI: 10.1016/j.chaos.2025.116133
Bruno R.R. Boaretto , Elbert E.N. Macau , Cristina Masoller
Extreme events are rare, large-scale deviations from typical system behavior that can occur in nonlinear dynamical systems. In this study, we explore the emergence of extreme events within a network of identical stochastic Hodgkin–Huxley neurons with mean-field coupling. The neurons are exposed to uncorrelated noise, which introduces stochastic electrical fluctuations that influence their spiking activity. Analyzing the variations in the amplitude of the mean field, we observe a smooth transition from small-amplitude, out-of-sync activity to synchronized spiking activity as the coupling parameter increases, while an abrupt transition occurs with increasing noise intensity. However, beyond a certain threshold, the coupling abruptly suppresses the spiking activity of the network. Our analysis reveals that the influence of noise combined with neuronal coupling near the abrupt transitions can trigger cascades of synchronized spiking activity, identified as extreme events. The analysis of the entropy of the mean field allows us to detect the parameter region where these events occur. We characterize the statistics of these events and find that, as the network size increases, the parameter range where they occur decreases significantly. Our findings shed light on the mechanisms driving extreme events in neural networks and how noise and neural coupling shape collective behavior.
{"title":"Noise-induced extreme events in Hodgkin–Huxley neural networks","authors":"Bruno R.R. Boaretto , Elbert E.N. Macau , Cristina Masoller","doi":"10.1016/j.chaos.2025.116133","DOIUrl":"10.1016/j.chaos.2025.116133","url":null,"abstract":"<div><div>Extreme events are rare, large-scale deviations from typical system behavior that can occur in nonlinear dynamical systems. In this study, we explore the emergence of extreme events within a network of identical stochastic Hodgkin–Huxley neurons with mean-field coupling. The neurons are exposed to uncorrelated noise, which introduces stochastic electrical fluctuations that influence their spiking activity. Analyzing the variations in the amplitude of the mean field, we observe a smooth transition from small-amplitude, out-of-sync activity to synchronized spiking activity as the coupling parameter increases, while an abrupt transition occurs with increasing noise intensity. However, beyond a certain threshold, the coupling abruptly suppresses the spiking activity of the network. Our analysis reveals that the influence of noise combined with neuronal coupling near the abrupt transitions can trigger cascades of synchronized spiking activity, identified as extreme events. The analysis of the entropy of the mean field allows us to detect the parameter region where these events occur. We characterize the statistics of these events and find that, as the network size increases, the parameter range where they occur decreases significantly. Our findings shed light on the mechanisms driving extreme events in neural networks and how noise and neural coupling shape collective behavior.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116133"},"PeriodicalIF":5.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454661","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}
Pub Date : 2025-02-21DOI: 10.1016/j.chaos.2025.116134
Zhengqiang Lu , Dehua Chen , Ruohua Gao , Stefano Boccaletti , Ludovico Minati , Zonghua Liu
In complex nervous systems such as the human brain, the structural and physiological connectivities are only partially correlated, and significant interdependence is observed between the activity of cortical regions that are not directly interconnected. A potential substrate for this decoupling is the phenomenon of remote synchronization, wherein non-adjacent node ensembles become preferentially entrained under suitable conditions. Early studies involving star graphs were grounded on a significant natural frequency mismatch between the hub and leaves. However, this requirement has poor ecological validity, that is, a substantial frequency difference between the hub and leaf nodes is not typically satisfied in biological neural networks. In this study, we propose a community network model comprising one hub community and multiple leaf communities, where all nodes share homogeneous frequencies. A time delay is applied exclusively to the connections associated with the hub community. It is found that the emergence of remote synchronization depends on the coupling strength and time delay matching. Additionally, periodic resonances are observed concerning the natural frequency as well as the time delay. These results are robust across different oscillators and can be accounted for using an equivalent star graph with time delay. By underlining the importance of time delays, a pervasive property of signal propagation in the brain, these results offer a new perspective on the intricate relationship between the configuration of structural couplings and resulting activity synchronization.
{"title":"A remote synchronization model of community networks with homogeneous frequencies","authors":"Zhengqiang Lu , Dehua Chen , Ruohua Gao , Stefano Boccaletti , Ludovico Minati , Zonghua Liu","doi":"10.1016/j.chaos.2025.116134","DOIUrl":"10.1016/j.chaos.2025.116134","url":null,"abstract":"<div><div>In complex nervous systems such as the human brain, the structural and physiological connectivities are only partially correlated, and significant interdependence is observed between the activity of cortical regions that are not directly interconnected. A potential substrate for this decoupling is the phenomenon of remote synchronization, wherein non-adjacent node ensembles become preferentially entrained under suitable conditions. Early studies involving star graphs were grounded on a significant natural frequency mismatch between the hub and leaves. However, this requirement has poor ecological validity, that is, a substantial frequency difference between the hub and leaf nodes is not typically satisfied in biological neural networks. In this study, we propose a community network model comprising one hub community and multiple leaf communities, where all nodes share homogeneous frequencies. A time delay is applied exclusively to the connections associated with the hub community. It is found that the emergence of remote synchronization depends on the coupling strength and time delay matching. Additionally, periodic resonances are observed concerning the natural frequency as well as the time delay. These results are robust across different oscillators and can be accounted for using an equivalent star graph with time delay. By underlining the importance of time delays, a pervasive property of signal propagation in the brain, these results offer a new perspective on the intricate relationship between the configuration of structural couplings and resulting activity synchronization.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116134"},"PeriodicalIF":5.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463931","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}
Pub Date : 2025-02-21DOI: 10.1016/j.chaos.2025.116137
P.S. Grinchuk, S.M. Danilova-Tretiak
The paper analyzes the correlation between the population of megacities and the size of the metro in these megacities. The correlation was found only for a sampling of large cities with an area of more than 1000 km2 with a number of metro stations of more than 41. For the first time, it was shown that for such a sampling of the largest megacities, consisting of 56 cities, there is a correlation between the number of metro stations St and the population of the city P of the form of the power law , where is the average number of people served by one station, is the exponent. It is shown that all cities in the sampling can be divided into 4 groups. Each group has approximately the same average number of people served by one station. It varies from to thousand people per station. The common features of cities included in different groups are discussed. It is assumed that the discovered correlation is of a fractal nature. It is shown that the fractal dimension of the external perimeter for a two-dimensional percolation cluster has a the same value. A qualitative model is proposed that can explain such fractal behavior for metro networks in megacities. It is shown that the discovered exponent in the correlation is close in value to the fundamental percolation constant (), which characterizes the most general topological properties of fractals, primarily such as connectivity close to critical point (Milovanov, 1997). A possible relation between the structure of large metro networks and this percolation constant is discussed. An analogy is shown between large metro networks and transport routes formed by ants in large anthills, as well as with branched polymer molecules.
{"title":"Fractal power law and polymer-like behavior for the metro growth in megacities","authors":"P.S. Grinchuk, S.M. Danilova-Tretiak","doi":"10.1016/j.chaos.2025.116137","DOIUrl":"10.1016/j.chaos.2025.116137","url":null,"abstract":"<div><div>The paper analyzes the correlation between the population of megacities and the size of the metro in these megacities. The correlation was found only for a sampling of large cities with an area of more than 1000 km<sup>2</sup> with a number of metro stations of more than 41. For the first time, it was shown that for such a sampling of the largest megacities, consisting of 56 cities, there is a correlation between the number of metro stations St and the population of the city P of the form of the power law <span><math><mrow><mi>S</mi><mi>t</mi><mo>≈</mo><msup><mrow><mrow><mo>(</mo><mi>P</mi><mo>/</mo><msub><mrow><mi>P</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>)</mo></mrow></mrow><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></msup></mrow></math></span>, where <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>∗</mo></mrow></msub></math></span> is the average number of people served by one station, <span><math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>≈</mo><mn>4</mn><mo>/</mo><mn>3</mn></mrow></math></span> is the exponent. It is shown that all cities in the sampling can be divided into 4 groups. Each group has approximately the same average number of people served by one station. It varies from <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>≈</mo><mn>120</mn></mrow></math></span> to <span><math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>≈</mo><mn>415</mn></mrow></math></span> thousand people per station. The common features of cities included in different groups are discussed. It is assumed that the discovered correlation is of a fractal nature. It is shown that the fractal dimension of the external perimeter for a two-dimensional percolation cluster has a the same value. A qualitative model is proposed that can explain such fractal behavior for metro networks in megacities. It is shown that the discovered exponent <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> in the correlation is close in value to the fundamental percolation constant <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span> (<span><math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>≈</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>≈</mo><mn>1</mn><mo>,</mo><mn>327</mn><mo>≈</mo><mn>4</mn><mo>/</mo><mn>3</mn></mrow></math></span>), which characterizes the most general topological properties of fractals, primarily such as connectivity close to critical point (Milovanov, 1997). A possible relation between the structure of large metro networks and this percolation constant is discussed. An analogy is shown between large metro networks and transport routes formed by ants in large anthills, as well as with branched polymer molecules.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116137"},"PeriodicalIF":5.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454660","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}
Pub Date : 2025-02-20DOI: 10.1016/j.chaos.2025.116100
Joao V. Merenda, Gonzalo Travieso, Odemir M. Bruno
Many studies have focused on understanding and exploring network behaviors and classifying their nodes. On the other hand, few works have concentrated on classifying networks as a whole. This task is increasingly important today, given the era of big data and data science, as well as the substantial amount of available information. Many classification problems have been modeled as networks, and properly classifying these networks can assist various fields such as biology, social sciences, and technology, among others. Several algorithms have been developed for extracting network features, including the deterministic tourist walk (DTW) algorithm. The DTW algorithm is an agent-based method that employs a walker (tourist) to traverse the network according to a deterministic walking rule. However, the traditional DTW algorithm has a significant limitation: it allows the tourist to visit only one node at each iteration, even if multiple nodes meet the walking rule criteria. This constraint restricts the amount of information collected and reduces the method’s effectiveness in capturing the full complexity of the network. To address this limitation, we introduce a novel method for network feature extraction based on the DTW algorithm: the deterministic tourist walk with bifurcations (DTWB). The DTWB method allows the tourist to visit multiple nodes simultaneously by introducing bifurcations into the deterministic walking rule. This enables a more efficient exploration of the network structure and the extraction of more comprehensive features. Furthermore, the statistics derived from this approach have revealed important patterns. Our results demonstrate that the DTWB method achieves remarkable performance in classifying both synthetic (theoretical) and real-world networks, with accuracy rates above 97% for synthetic networks and close to 100% when using certain feature combinations. For real-world networks, the performance varies by dataset, ranging from 85.9% to 99.4%. A comparison with other methods shows that the DTWB method performs better on datasets with greater variance in the number of nodes, which is characteristic of most real-world networks.
{"title":"Pattern recognition on networks using bifurcated deterministic self-avoiding walks","authors":"Joao V. Merenda, Gonzalo Travieso, Odemir M. Bruno","doi":"10.1016/j.chaos.2025.116100","DOIUrl":"10.1016/j.chaos.2025.116100","url":null,"abstract":"<div><div>Many studies have focused on understanding and exploring network behaviors and classifying their nodes. On the other hand, few works have concentrated on classifying networks as a whole. This task is increasingly important today, given the era of big data and data science, as well as the substantial amount of available information. Many classification problems have been modeled as networks, and properly classifying these networks can assist various fields such as biology, social sciences, and technology, among others. Several algorithms have been developed for extracting network features, including the deterministic tourist walk (DTW) algorithm. The DTW algorithm is an agent-based method that employs a walker (tourist) to traverse the network according to a deterministic walking rule. However, the traditional DTW algorithm has a significant limitation: it allows the tourist to visit only one node at each iteration, even if multiple nodes meet the walking rule criteria. This constraint restricts the amount of information collected and reduces the method’s effectiveness in capturing the full complexity of the network. To address this limitation, we introduce a novel method for network feature extraction based on the DTW algorithm: the deterministic tourist walk with bifurcations (DTWB). The DTWB method allows the tourist to visit multiple nodes simultaneously by introducing bifurcations into the deterministic walking rule. This enables a more efficient exploration of the network structure and the extraction of more comprehensive features. Furthermore, the statistics derived from this approach have revealed important patterns. Our results demonstrate that the DTWB method achieves remarkable performance in classifying both synthetic (theoretical) and real-world networks, with accuracy rates above 97% for synthetic networks and close to 100% when using certain feature combinations. For real-world networks, the performance varies by dataset, ranging from 85.9% to 99.4%. A comparison with other methods shows that the DTWB method performs better on datasets with greater variance in the number of nodes, which is characteristic of most real-world networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116100"},"PeriodicalIF":5.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445230","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}
Pub Date : 2025-02-20DOI: 10.1016/j.chaos.2025.116113
Ding Chen , Mengjun Mei , Jin Jiang , Cheng Wang
In view of the limitations of fractal models with single fractal dimension in representing the spatial non-uniform distribution of urban rail transit network, a segmented fractal model is established by summarizing the variation patterns of inflection points in network length curves and the definition of binary classification in spatial distribution analysis. This model adheres to the countable additivity definition of the measurement for disjoint fractal sets and retains the inherent measurement relationship in fractal theory. By examining the results of spatial distribution analysis derived from typical urban rail transit network data, the correlation between model parameters and spatial distribution characteristics is investigated. This process validates the effectiveness of the model while also exploring the physical meaning of its parameters. The results show that the segmented point in this model divides the network into two domains. The fractal dimensions corresponding to the first and second domains are relatively independent and can be utilized to characterize the spatial heterogeneous growth rate of the network. Segmented point in this model is identified as the main parameter that exhibits significant positive correlations with the spatial distribution characteristics, including the standard deviation distance, semi-major axis and semi-minor axis. The correlation coefficients are 0.89, 0.90, and 0.75, respectively. These results indicate that the network located within the first domain demonstrates an aggregation distribution characteristic, whereas that within the second domain exhibits a dispersion distribution characteristic. Besides, the parameters in the model have been found to inadequately reflect the intensity of directional distribution within the network. However, the segmented point within these model parameters can serve as an indicator for the coverage range of a directionally distributed network along both its semi-major and semi-minor axes.
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