Chaos Solitons & Fractals最新文献

英文中文

Revealing consistent patterns and intrinsic mechanisms of subway systems via relative influence

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116186

Ting Yu , Liang Gao , Chaoyang Zhang , Shixin Chang , Xiao Han , Bingfeng Si , Jose F.F. Mendes

Subway systems play a vital role in facilitating mobility within cities. However, the complex, nonlinear interactions between subway stations are difficult to capture using traditional approaches, which typically focus on static network structures or absolute passenger flow. These methods fail to adequately address the dynamic nature of subway systems and hinder cross-city comparisons. In this study, we integrate perspectives from dynamics and system science to quantify the relative influence between subway stations, accounting for both network connectivity and dynamic characteristics. This approach effectively eliminates biases related to city scale, allowing for meaningful cross-city comparisons. Additionally, we develop a simulation model that links individual travel behavior with collective-level phenomena, shedding light on the intrinsic mechanisms governing passenger flow. By analyzing relative influence, we define a station importance metric that reveals the functional roles of stations within the network. Empirical analyses of subway systems in Beijing, Chongqing, Nanjing, and Suzhou demonstrate consistent patterns in relative influence distributions across cities and time periods. These patterns align with a time-based, two-step preferential attachment mechanism governing passenger travel. A comparison of our proposed station importance metric with traditional centrality measures further validates its effectiveness. This research provides valuable insights into subway network operations, contributing to the optimization of system resilience and management strategies.

{"title":"Revealing consistent patterns and intrinsic mechanisms of subway systems via relative influence","authors":"Ting Yu , Liang Gao , Chaoyang Zhang , Shixin Chang , Xiao Han , Bingfeng Si , Jose F.F. Mendes","doi":"10.1016/j.chaos.2025.116186","DOIUrl":"10.1016/j.chaos.2025.116186","url":null,"abstract":"<div><div>Subway systems play a vital role in facilitating mobility within cities. However, the complex, nonlinear interactions between subway stations are difficult to capture using traditional approaches, which typically focus on static network structures or absolute passenger flow. These methods fail to adequately address the dynamic nature of subway systems and hinder cross-city comparisons. In this study, we integrate perspectives from dynamics and system science to quantify the relative influence between subway stations, accounting for both network connectivity and dynamic characteristics. This approach effectively eliminates biases related to city scale, allowing for meaningful cross-city comparisons. Additionally, we develop a simulation model that links individual travel behavior with collective-level phenomena, shedding light on the intrinsic mechanisms governing passenger flow. By analyzing relative influence, we define a station importance metric that reveals the functional roles of stations within the network. Empirical analyses of subway systems in Beijing, Chongqing, Nanjing, and Suzhou demonstrate consistent patterns in relative influence distributions across cities and time periods. These patterns align with a time-based, two-step preferential attachment mechanism governing passenger travel. A comparison of our proposed station importance metric with traditional centrality measures further validates its effectiveness. This research provides valuable insights into subway network operations, contributing to the optimization of system resilience and management strategies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116186"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511409","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}

引用次数: 0

Quadratic solitons in higher-order topological insulators

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116199

Yaroslav V. Kartashov

I consider higher-order topological insulator (HOTI) created in

χ^{(2)}

nonlinear medium and based on two-dimensional generalization of the Su-Schrieffer-Heeger waveguide array, where transition between trivial and topological phases is achieved by shift of the four waveguides in the unit cell towards its center or towards its periphery. Such HOTI can support linear topological corner states that give rise to rich families of quadratic topological solitons bifurcating from linear corner states. The presence of phase mismatch between parametrically interacting fundamental-frequency (FF) and second-harmonic (SH) waves drastically affects the bifurcation scenarios and domains of soliton existence, making the families of corner solitons much richer in comparison with those in HOTIs with cubic nonlinearity. For instance, the internal soliton structure strongly depends on the location of propagation constant in forbidden gaps in spectra of both FF and SH waves. Two different types of corner solitons are obtained, where either FF or SH wave dominates in the bifurcation point from linear corner state. Because the waveguides are two-mode for SH wave, its spectrum features two groups of forbidden gaps with corner states of different symmetry appearing in each of them. Such corner states give rise to different families of corner solitons. Stability analysis shows that corner solitons in quadratic HOTI may feature wide stability domains and therefore are observable experimentally. These results illustrate how parametric nonlinear interactions enrich the behavior of topological excitations and allow to control their shapes.

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引用次数: 0

Unraveling the dynamical mechanisms of motor preparation based on the heterogeneous attractor model

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116220

Xiaomeng Wang , Lining Yin , Ying Yu , Qingyun Wang

Different types of inhibitory interneurons play a crucial role in regulating the reaction time and accuracy of voluntary movements. To explore the neurodynamic mechanisms underlying this regulation, we construct a cortical inhibitory microcircuit model, comprising excitatory preparatory and executive nuclei as well as three inhibitory interneuron nuclei. It replicates the neural activity patterns in the motor cortex during movement preparation and execution observed in physiological experiments, as along with activity changes induced by learning. We analyze the effects of inhibitory synaptic strength and inhibitory neuron self-firing rate on voluntary movement in the model. Our findings reveal that the inhibitory synaptic strength of somatostatin (SST) and parvalbumin (PV) neurons on pyramidal cells (PC) can significantly affect reaction time. By regulating their firing rates, the ratio of the inhibitory effects of SST and PV can improve the response speed and the accuracy of motion selection. Further analysis indicates that SST-dominated selection leads to quicker but less accurate responses, whereas PV-dominated selection produces slower but more precise outcomes. Finally, using a mean-field approach, we find that the stabilization points and attraction domains of the system are different in the preparation and execution phase. Learning expands the attraction domain for choosing correctly in the preparation and execution phases and the equilibrium point for choosing failures disappears, improving the speed of reaction and the rate of correct choices. Our model gives new insights into the dynamics of inhibitory networks in voluntary movement control and learning.

{"title":"Unraveling the dynamical mechanisms of motor preparation based on the heterogeneous attractor model","authors":"Xiaomeng Wang , Lining Yin , Ying Yu , Qingyun Wang","doi":"10.1016/j.chaos.2025.116220","DOIUrl":"10.1016/j.chaos.2025.116220","url":null,"abstract":"<div><div>Different types of inhibitory interneurons play a crucial role in regulating the reaction time and accuracy of voluntary movements. To explore the neurodynamic mechanisms underlying this regulation, we construct a cortical inhibitory microcircuit model, comprising excitatory preparatory and executive nuclei as well as three inhibitory interneuron nuclei. It replicates the neural activity patterns in the motor cortex during movement preparation and execution observed in physiological experiments, as along with activity changes induced by learning. We analyze the effects of inhibitory synaptic strength and inhibitory neuron self-firing rate on voluntary movement in the model. Our findings reveal that the inhibitory synaptic strength of somatostatin (SST) and parvalbumin (PV) neurons on pyramidal cells (PC) can significantly affect reaction time. By regulating their firing rates, the ratio of the inhibitory effects of SST and PV can improve the response speed and the accuracy of motion selection. Further analysis indicates that SST-dominated selection leads to quicker but less accurate responses, whereas PV-dominated selection produces slower but more precise outcomes. Finally, using a mean-field approach, we find that the stabilization points and attraction domains of the system are different in the preparation and execution phase. Learning expands the attraction domain for choosing correctly in the preparation and execution phases and the equilibrium point for choosing failures disappears, improving the speed of reaction and the rate of correct choices. Our model gives new insights into the dynamics of inhibitory networks in voluntary movement control and learning.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116220"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511411","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}

引用次数: 0

Long-range interaction of kinks in higher-order polynomial models

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116170

Ekaterina Belendryasova , Petr A. Blinov , Tatiana V. Gani , Alexander A. Malnev , Vakhid A. Gani

We obtain asymptotic estimates of the interaction forces between kink and antikink in a family of field-theoretic models with two vacua in (1+1)-dimensional space–time. In our study we consider a new class of soliton solutions previously found in our paper (Chaos Solitons Fractals 2022;165:112805). We focus on the case of kinks having one exponential and one power-law asymptotics. We show that if the kink and antikink are faced each other with long-range tails, the force of attraction between them at large separations demonstrates a power-law decay with the distance. We also performed numerical simulations to measure the interaction force and obtained good agreement between the experimental values and theoretical estimates.

引用次数: 0

Dynamics of a neuron with a hybrid memristive ion channel

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116233

Zhenhua Yu , Kailong Zhu , Ya Wang , Feifei Yang

From the viewpoint of the physical, the membrane potential of the biological neuron can be effectively expressed by applying a capacitor. The ion channel in the neuron model can be selected the electrical element the relative to electromagnetic field to estimate and describe. In this paper, a hybrid memristive ion channel is built by connecting an inductor in series to a charge-controlled memristor (CCM), and a neural circuit with a hybrid memristive ion channel is designed by paralleling a capacitor and a nonlinear resistor to both sides of the hybrid memristive ion channel. Furthermore, the oscillator model of neural circuit and its energy function are derived by using the Kirchhoff's Current Law (KCL), Kirchhoff's Voltage Law (KVL) and Helmholtz's theorem. Furthermore, an adaptive regulation law is designed for investigating the self-regulation of neurons. The results illustrate that electrical activities of the neuron model with a hybrid memristive ion channel can be controlled by the external electric field distribution, and its firing modes are also adjusted by the energy ratio of the capacitor to the total energy in the neural circuit. This study is helpful to build artificial neurons with mixed ion channels.

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引用次数: 0

Novel soliton solutions of the (3+1)-dimensional stochastic nonlinear Schrödinger equation in birefringent fibers

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116152

Elsayed M.E. Zayed , Manar S. Ahmed , Ahmed H. Arnous , Yakup Yıldırım

The paper studies novel solitary waves with the

(3 + 1)

-dimensional nonlinear Schrödinger equation in birefringent fibers having a white noise effect. This model is reported in this paper for the first time, guaranteeing that the analysis and results are novel and original. To investigate this model, we implement two techniques, namely, the projective Riccati equation method and the enhanced direct algebraic method. The obtained solutions are bright solitons, dark solitons, singular solitons, and straddled solitons. Besides these solitons, Jacobi and Weierstrass elliptic solutions are also obtained. These findings expand our understanding of nonlinear wave propagation in birefringent fibers under the influence of white noise and introduce new mathematical methods for solving complex nonlinear differential equations. The study opens up new directions for future research in nonlinear optical phenomena, encouraging the exploration of other nonlinear models in optical fibers and beyond.

{"title":"Novel soliton solutions of the (3+1)-dimensional stochastic nonlinear Schrödinger equation in birefringent fibers","authors":"Elsayed M.E. Zayed , Manar S. Ahmed , Ahmed H. Arnous , Yakup Yıldırım","doi":"10.1016/j.chaos.2025.116152","DOIUrl":"10.1016/j.chaos.2025.116152","url":null,"abstract":"<div><div>The paper studies novel solitary waves with the <span><math><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional nonlinear Schrödinger equation in birefringent fibers having a white noise effect. This model is reported in this paper for the first time, guaranteeing that the analysis and results are novel and original. To investigate this model, we implement two techniques, namely, the projective Riccati equation method and the enhanced direct algebraic method. The obtained solutions are bright solitons, dark solitons, singular solitons, and straddled solitons. Besides these solitons, Jacobi and Weierstrass elliptic solutions are also obtained. These findings expand our understanding of nonlinear wave propagation in birefringent fibers under the influence of white noise and introduce new mathematical methods for solving complex nonlinear differential equations. The study opens up new directions for future research in nonlinear optical phenomena, encouraging the exploration of other nonlinear models in optical fibers and beyond.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116152"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520050","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}

引用次数: 0

Discovering overlapping communities in multi-layer directed networks

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-28 DOI: 10.1016/j.chaos.2025.116175

Huan Qing

Community detection in multi-layer undirected networks has attracted considerable attention in recent years. However, multi-layer directed networks are common in the real world, and existing community detection methods often either ignore the asymmetric structure in multi-layer directed networks or assume that every node solely belongs to a single community, significantly limiting their applicability to overlapping multi-layer directed networks, where nodes can belong to multiple communities simultaneously. To fill this gap, this article explores the challenging problem of detecting overlapping communities in multi-layer directed networks. Our goal is to understand the underlying asymmetric overlapping community structure by analyzing the mixed memberships of nodes. We introduce a novel multi-layer mixed membership stochastic co-block model (multi-layer MM-ScBM) to model overlapping multi-layer directed networks. We develop a spectral procedure to estimate nodes’ memberships in both sending and receiving patterns. Our method uses a successive projection algorithm on a few leading eigenvectors of two debiased aggregation matrices. To our knowledge, this is the first work to detect asymmetric overlapping communities in multi-layer directed networks. We demonstrate the consistent estimation properties of our method by providing per-node error rates under the multi-layer MM-ScBM framework. Our theoretical analysis reveals that increasing the overall sparsity, the number of nodes, or the number of layers can improve the accuracy of overlapping community detection. Extensive numerical experiments validate these theoretical findings. We also apply our method to one real-world multi-layer directed network, gaining insightful results.

{"title":"Discovering overlapping communities in multi-layer directed networks","authors":"Huan Qing","doi":"10.1016/j.chaos.2025.116175","DOIUrl":"10.1016/j.chaos.2025.116175","url":null,"abstract":"<div><div>Community detection in multi-layer undirected networks has attracted considerable attention in recent years. However, multi-layer directed networks are common in the real world, and existing community detection methods often either ignore the asymmetric structure in multi-layer directed networks or assume that every node solely belongs to a single community, significantly limiting their applicability to overlapping multi-layer directed networks, where nodes can belong to multiple communities simultaneously. To fill this gap, this article explores the challenging problem of detecting overlapping communities in multi-layer directed networks. Our goal is to understand the underlying asymmetric overlapping community structure by analyzing the mixed memberships of nodes. We introduce a novel multi-layer mixed membership stochastic co-block model (multi-layer MM-ScBM) to model overlapping multi-layer directed networks. We develop a spectral procedure to estimate nodes’ memberships in both sending and receiving patterns. Our method uses a successive projection algorithm on a few leading eigenvectors of two debiased aggregation matrices. To our knowledge, this is the first work to detect asymmetric overlapping communities in multi-layer directed networks. We demonstrate the consistent estimation properties of our method by providing per-node error rates under the multi-layer MM-ScBM framework. Our theoretical analysis reveals that increasing the overall sparsity, the number of nodes, or the number of layers can improve the accuracy of overlapping community detection. Extensive numerical experiments validate these theoretical findings. We also apply our method to one real-world multi-layer directed network, gaining insightful results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116175"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511408","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}

引用次数: 0

Frustration induced chimeras and motion in two dimensional swarmalators

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-27 DOI: 10.1016/j.chaos.2025.116164

R. Senthamizhan, R. Gopal, V.K. Chandrasekar

Swarmalators are oscillators that combine the properties of swarming systems and coupled oscillators, providing a framework to study systems where individual agents synchronize their internal states and simultaneously organize their spatial positions, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering where swarmalators split into distinct groups that exhibit synchronized and unsynchronized behavior, both in their oscillatory phases and spatial positions, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.

{"title":"Frustration induced chimeras and motion in two dimensional swarmalators","authors":"R. Senthamizhan, R. Gopal, V.K. Chandrasekar","doi":"10.1016/j.chaos.2025.116164","DOIUrl":"10.1016/j.chaos.2025.116164","url":null,"abstract":"<div><div>Swarmalators are oscillators that combine the properties of swarming systems and coupled oscillators, providing a framework to study systems where individual agents synchronize their internal states and simultaneously organize their spatial positions, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering where swarmalators split into distinct groups that exhibit synchronized and unsynchronized behavior, both in their oscillatory phases and spatial positions, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116164"},"PeriodicalIF":5.3,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508183","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}

引用次数: 0

Oscillating Turing patterns, chaos and strange attractors in a reaction–diffusion system augmented with self- and cross-diffusion terms

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-27 DOI: 10.1016/j.chaos.2025.116181

Benjamin Aymard

In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and orbits of the latter. Special attention is paid to accuracy, a necessary condition when one wants to catch periodic orbits and to perform their linear stability analysis via Floquet multipliers. Bifurcations with respect to a single control parameter are studied in four different regimes of diffusion: linear diffusion, self-diffusion for each of the two species, and cross-diffusion. Key observations are made: development of original Turing patterns, supercritical Hopf bifurcations leading to oscillating patterns and period doubling cascades leading to chaos. Eventually, original strange attractors are reported in phase space.

引用次数: 0

Large enhancement of nonlinear optical response of graphene nanoribbon heterojunctions with multiple topological interface states

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-02-27 DOI: 10.1016/j.chaos.2025.116176

Hanying Deng , Yaxin Li , Zhihao Qu , Jing Deng , Yingji He , Fangwei Ye

We investigate the nonlinear optical response of graphene nanoribbon (GNR) heterojunctions both without and with one or multiple topological interface states. By implementing a distant-neighbor quantum-mechanical (DNQM) method, we demonstrate a pronounced enhancement of the nonlinear optical response of GNR heterojunctions as the number of topological states at their interfaces increases. Specifically, we find that GNR heterojunctions with multiple topological interface states exhibit a notably stronger third-order nonlinear optical response in comparison with their similarly sized counterparts with a single topological interface state or without such states. Furthermore, we observe that the presence of topological interface states in GNR heterojunctions can induce a significant red-shift of the resonance frequency of their linear and nonlinear optical response. Our results reveal the potential to enhance the nonlinear optical response at the nanoscale by increasing the number of topological interface states in graphene nanostructures or other topological systems.

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引用次数: 0

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Chaos Solitons & Fractals

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