Pub Date : 2025-02-01DOI: 10.1016/j.chaos.2024.115904
Iram Hussan , Manyu Zhao , Xu Zhang
Since the memristor is a natural system with memory effects, the introduction of memristors into nonlinear systems brings very different dynamics compared with classical ones, and inspires the development of applications of memristors. In this article, a kind of maps via the combination of two memristors is studied. This class of memristive maps is three-dimensional (3D) and has the coexistence of infinitely many hyperchaotic attractors under certain conditions, where each attractor has two positive Lyapunov exponents.
{"title":"Two-memristor-based maps with infinitely many hyperchaotic attractors","authors":"Iram Hussan , Manyu Zhao , Xu Zhang","doi":"10.1016/j.chaos.2024.115904","DOIUrl":"10.1016/j.chaos.2024.115904","url":null,"abstract":"<div><div>Since the memristor is a natural system with memory effects, the introduction of memristors into nonlinear systems brings very different dynamics compared with classical ones, and inspires the development of applications of memristors. In this article, a kind of maps via the combination of two memristors is studied. This class of memristive maps is three-dimensional (3D) and has the coexistence of infinitely many hyperchaotic attractors under certain conditions, where each attractor has two positive Lyapunov exponents.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115904"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857621","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115902
Shu Guo, Jing Lyu, Xuebin Zhu, Hanwen Fan
Node importance has been a widespread research topic owing to the impact of uncertainties and accidents on supply chains during maritime transport. Although the analysis and investigation of critical nodes using complex network theory is mature and systematic, there is often a lack of multiscale node identification models and theoretical frameworks. This paper proposes a novel quantitative analysis framework and process for node importance by fusing multiple features. Node importance is determined by interdependence, risk sensitivity, and spatial conflict. These three dimensions consider the network topology, node robustness, and transportation environment stability. A case study of the Belt and Road Initiative shipping network verified the validity and feasibility of this framework. The results indicated that the importance of nodes can be represented by their heterogeneity. Critical regions strongly coincide with the distribution of major global straits and transportation routes. Notably, the similarity of results under multi-features improves the accuracy of identifying critical nodes and regions within the complex network, whereas the differences compensate for the shortcomings of the single-dimensional approach. This provides actionable insights and guidance for stakeholders to build stability in maritime supply chains.
{"title":"Multi-feature fusion for the evaluation of strategic nodes and regional importance in maritime networks","authors":"Shu Guo, Jing Lyu, Xuebin Zhu, Hanwen Fan","doi":"10.1016/j.chaos.2024.115902","DOIUrl":"10.1016/j.chaos.2024.115902","url":null,"abstract":"<div><div>Node importance has been a widespread research topic owing to the impact of uncertainties and accidents on supply chains during maritime transport. Although the analysis and investigation of critical nodes using complex network theory is mature and systematic, there is often a lack of multiscale node identification models and theoretical frameworks. This paper proposes a novel quantitative analysis framework and process for node importance by fusing multiple features. Node importance is determined by interdependence, risk sensitivity, and spatial conflict. These three dimensions consider the network topology, node robustness, and transportation environment stability. A case study of the Belt and Road Initiative shipping network verified the validity and feasibility of this framework. The results indicated that the importance of nodes can be represented by their heterogeneity. Critical regions strongly coincide with the distribution of major global straits and transportation routes. Notably, the similarity of results under multi-features improves the accuracy of identifying critical nodes and regions within the complex network, whereas the differences compensate for the shortcomings of the single-dimensional approach. This provides actionable insights and guidance for stakeholders to build stability in maritime supply chains.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115902"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857623","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115891
Yuzhuo Zhao , Dan Ma
An adaptive finite-time prescribed performance control (FTPPC) strategy is considered based on the time-delay neural network (NN) observer for the uncertain nonlinear system with unknown time-delay. Unlike previous works, a time-delay NN state observer based on the existing NN state observer is proposed, which not only solves the problem of the linear observer being unable to accurately observe the system states, but also extends the NN state observer without the time-delay to the time-delay NN state observer for the nonlinear system with state time-delay. What is more, instead of traditional Krasovskii functionals, the finite covering lemma and the RBF NN are combined to approximate unknown nonlinear time-delay functions. In addition, an adaptive FTPPC method is proposed by using the finite-time performance function (FTPF), which ensures the dynamic performance of the system while ensures the steady-state performance of the system in finite time. Among them, the stability time can be arbitrarily given, which means it does not rely on any parameter value. Finally, the electromechanical system is utilized to verify the effectiveness of the proposed strategy.
{"title":"Time-delay neural network observer-based adaptive finite-time prescribed performance control for nonlinear systems with unknown time-delay","authors":"Yuzhuo Zhao , Dan Ma","doi":"10.1016/j.chaos.2024.115891","DOIUrl":"10.1016/j.chaos.2024.115891","url":null,"abstract":"<div><div>An adaptive finite-time prescribed performance control (FTPPC) strategy is considered based on the time-delay neural network (NN) observer for the uncertain nonlinear system with unknown time-delay. Unlike previous works, a time-delay NN state observer based on the existing NN state observer is proposed, which not only solves the problem of the linear observer being unable to accurately observe the system states, but also extends the NN state observer without the time-delay to the time-delay NN state observer for the nonlinear system with state time-delay. What is more, instead of traditional Krasovskii functionals, the finite covering lemma and the RBF NN are combined to approximate unknown nonlinear time-delay functions. In addition, an adaptive FTPPC method is proposed by using the finite-time performance function (FTPF), which ensures the dynamic performance of the system while ensures the steady-state performance of the system in finite time. Among them, the stability time can be arbitrarily given, which means it does not rely on any parameter value. Finally, the electromechanical system is utilized to verify the effectiveness of the proposed strategy.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115891"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857629","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115810
Runze Jiang , Pengjian Shang , Yi Yin
Entropy serves as an effective method for quantifying the irregularity and complexity of nonlinear time series or complex signals. Recently, a novel entropy measure, attention entropy (AE), has been introduced for detecting interbeat interval time series. However, the original AE focuses solely on peak points, potentially overlooking crucial information embedded in signals. In this paper, we present the global ordinal pattern attention entropy (GOPAE), a novel measure that integrates AE with the principles of phase space reconstruction (PSR). Additionally, the connections between GOPAE and state-of-the-art time series network methods, including ordinal pattern transition network (OPTN) and recurrence quantification analysis (RQA), are elucidated to showcase its proficiency in extracting dynamic information from complex signals. Comparative experiments, both qualitative and quantitative, are conducted, using both simulated data and real-world signals. The results of the experiments suggest that GOPAE can effectively distinguishing complex signals in real application scenarios.
{"title":"Global ordinal pattern attention entropy: A novel feature extraction method for complex signals","authors":"Runze Jiang , Pengjian Shang , Yi Yin","doi":"10.1016/j.chaos.2024.115810","DOIUrl":"10.1016/j.chaos.2024.115810","url":null,"abstract":"<div><div>Entropy serves as an effective method for quantifying the irregularity and complexity of nonlinear time series or complex signals. Recently, a novel entropy measure, attention entropy (AE), has been introduced for detecting interbeat interval time series. However, the original AE focuses solely on peak points, potentially overlooking crucial information embedded in signals. In this paper, we present the global ordinal pattern attention entropy (GOPAE), a novel measure that integrates AE with the principles of phase space reconstruction (PSR). Additionally, the connections between GOPAE and state-of-the-art time series network methods, including ordinal pattern transition network (OPTN) and recurrence quantification analysis (RQA), are elucidated to showcase its proficiency in extracting dynamic information from complex signals. Comparative experiments, both qualitative and quantitative, are conducted, using both simulated data and real-world signals. The results of the experiments suggest that GOPAE can effectively distinguishing complex signals in real application scenarios.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115810"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815846","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115854
Yong-Kai Liu , Ying-Feng Gao , Ning Yue , Shi-Jie Yang
A vortex molecule is predicted in a spin–orbit-coupled spin-1 Bose–Einstein condensate. This type of asymmetric soliton features four off-axis vortices and none of them coincide. There are two vortices of the same charge in the first and the third component, respectively, and two vortices of the opposite charge in the second component. This particular arrangement of vortices constitute a spin vortex molecule which is connected by a domain wall in the spin texture. In the dynamical simulation, we find the vortex molecule is static at the equilibrium but vibrates once it deviates from the equilibrium. The vibration mechanism is identified: fragmentation and coalescence. The vortex molecule exhibits mixing of ferromagnetic and antiferromagnetic states, where the meron-pair or bimeron is hidden. Our results suggest a way of creating bimeron-like vortex molecules in spin-1 Bose–Einstein condensates.
{"title":"Vortex molecules in a spin–orbit-coupled spin-1 condensate","authors":"Yong-Kai Liu , Ying-Feng Gao , Ning Yue , Shi-Jie Yang","doi":"10.1016/j.chaos.2024.115854","DOIUrl":"10.1016/j.chaos.2024.115854","url":null,"abstract":"<div><div>A vortex molecule is predicted in a spin–orbit-coupled spin-1 Bose–Einstein condensate. This type of asymmetric soliton features four off-axis vortices and none of them coincide. There are two vortices of the same charge in the first and the third component, respectively, and two vortices of the opposite charge in the second component. This particular arrangement of vortices constitute a spin vortex molecule which is connected by a domain wall in the spin texture. In the dynamical simulation, we find the vortex molecule is static at the equilibrium but vibrates once it deviates from the equilibrium. The vibration mechanism is identified: fragmentation and coalescence. The vortex molecule exhibits mixing of ferromagnetic and antiferromagnetic states, where the meron-pair or bimeron is hidden. Our results suggest a way of creating bimeron-like vortex molecules in spin-1 Bose–Einstein condensates.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115854"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815866","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115849
Rumi Kar , V.K. Chandrasekar , D.V. Senthilkumar
We investigate the collective dynamics of a network comprising two populations of globally coupled phase oscillators with intrinsic frequency heterogeneity and varying fractions of pairwise and higher-order interactions. Our results show that, with homogeneous phase lag parameters, increasing the fraction of higher-order interactions and coupling strength leads to more complex dynamics, including distinct monostable and bistable chimera regions. Considering the heterogeneity of the phase lag parameter between pairwise and higher-order interactions, our study reveals that increasing the fraction of higher-order interactions leads to the emergence of various bistable and multistable regions while destabilizing monostable chimera regions, especially at small coupling strengths. Conversely, increasing the coupling strength has minimal impact on the system’s dynamics for small fractions of higher-order interactions, whereas a larger fraction of higher-order interactions uncovers additional bistable and multistable regions. We derive low-dimensional reduced equations from the -dimensional discrete system using the Ott–Antonsen ansatz and obtain bifurcation curves using XPPAUT software. Additionally, we deduce stability conditions for both synchronized and desynchronized states, which align precisely with the numerical results.
{"title":"Effect of heterogeneities in two-populations of globally coupled phase oscillators with higher-order interaction","authors":"Rumi Kar , V.K. Chandrasekar , D.V. Senthilkumar","doi":"10.1016/j.chaos.2024.115849","DOIUrl":"10.1016/j.chaos.2024.115849","url":null,"abstract":"<div><div>We investigate the collective dynamics of a network comprising two populations of globally coupled phase oscillators with intrinsic frequency heterogeneity and varying fractions of pairwise and higher-order interactions. Our results show that, with homogeneous phase lag parameters, increasing the fraction of higher-order interactions and coupling strength leads to more complex dynamics, including distinct monostable and bistable chimera regions. Considering the heterogeneity of the phase lag parameter between pairwise and higher-order interactions, our study reveals that increasing the fraction of higher-order interactions leads to the emergence of various bistable and multistable regions while destabilizing monostable chimera regions, especially at small coupling strengths. Conversely, increasing the coupling strength has minimal impact on the system’s dynamics for small fractions of higher-order interactions, whereas a larger fraction of higher-order interactions uncovers additional bistable and multistable regions. We derive low-dimensional reduced equations from the <span><math><mi>N</mi></math></span>-dimensional discrete system using the Ott–Antonsen ansatz and obtain bifurcation curves using XPPAUT software. Additionally, we deduce stability conditions for both synchronized and desynchronized states, which align precisely with the numerical results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115849"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815829","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115878
Xiaoyue Wang , Zhixue He , Ju Chen , Mingjuan Zhang , Lei Shi
Social cohesion, defined by mutual cooperation and robust social connections, is fundamental for addressing collective challenges. With the growing prevalence of inequality in modern societies, its potential impact on the formation of social cohesion cannot be overlooked. This study investigates social cohesion within a population by incorporating individuals with binary endowments (including both rich and poor) into a migration model. Individuals’ migration decisions are driven by both peer preference and payoff pursuit. Our results reveal diverse spatial patterns: while peer preference leads to small, scattered clusters, payoff pursuit promotes spontaneous aggregation and sustains high levels of cooperation within the population, thereby enhancing social cohesion. In particular, interactions between rich and poor are critical for maintaining large-scale cooperation during self-organizing movements. However, excessive greed – manifested as high expectations or a strong pursuit of personal gain – can undermine social cohesion. Moreover, increasing endowment inequality further suppresses cooperation, weakening social cohesion. This study reveals the dynamics of social cohesion in populations with unequal endowments and provides new insights into the formation of social interaction, such as aggregation and segregation, through the lens of individual preferences.
{"title":"Balancing peer preference and payoff pursuit in migration shapes social cohesion within unequal endowment populations","authors":"Xiaoyue Wang , Zhixue He , Ju Chen , Mingjuan Zhang , Lei Shi","doi":"10.1016/j.chaos.2024.115878","DOIUrl":"10.1016/j.chaos.2024.115878","url":null,"abstract":"<div><div>Social cohesion, defined by mutual cooperation and robust social connections, is fundamental for addressing collective challenges. With the growing prevalence of inequality in modern societies, its potential impact on the formation of social cohesion cannot be overlooked. This study investigates social cohesion within a population by incorporating individuals with binary endowments (including both rich and poor) into a migration model. Individuals’ migration decisions are driven by both peer preference and payoff pursuit. Our results reveal diverse spatial patterns: while peer preference leads to small, scattered clusters, payoff pursuit promotes spontaneous aggregation and sustains high levels of cooperation within the population, thereby enhancing social cohesion. In particular, interactions between rich and poor are critical for maintaining large-scale cooperation during self-organizing movements. However, excessive greed – manifested as high expectations or a strong pursuit of personal gain – can undermine social cohesion. Moreover, increasing endowment inequality further suppresses cooperation, weakening social cohesion. This study reveals the dynamics of social cohesion in populations with unequal endowments and provides new insights into the formation of social interaction, such as aggregation and segregation, through the lens of individual preferences.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115878"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815853","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115912
Jhoana P. Romero-Leiton , Alissen Peterson , Pablo Aguirre , Carlos Bastidas-Caldes , Bouchra Nasri
The surge in antimicrobial resistance (AMR) is a critical global public health concern that complicates the eradication of harmful microorganisms within the host. Therefore, mathematical models have enhanced our understanding of AMR dynamics and aided in identifying measures to combat bacterial diseases, primarily focusing on single bacterial strains rather than microbial consortia. However, microbial consortia have not been extensively investigated. This study is a significant effort to examine the transmission of resistance in microbial communities, with a special focus on the ecological dynamics of microbial competition and the role of the host immune system in eradicating infections. We propose a mathematical model of AMR propagation that considers competition between two bacterial strains of the same species. Our analysis focuses on stability studies and the existence of bifurcations using different parameter values to represent the rate at which the host immune system eliminates bacteria. Our findings revealed that AMR propagation is primarily influenced by bacterial replication rate and host immune system efficacy. We observed that bacteria with lower replication rates could be effectively controlled, leading to disease extinction, whereas those with higher replication rates required a significantly robust immune response for clearance. The model demonstrated the existence of nine biologically feasible equilibrium points, with four explicitly associated with the different types of host immune systems characterized in the literature. Therefore, our study highlights the interplay between bacterial competition, immune system effectiveness, and AMR spread. We emphasize the importance of maintaining a robust immune system and establishing sensible antibiotic usage guidelines to slow the development and spread of antibiotic resistance.
{"title":"Dynamics of AMR beyond a single bacterial strain: Revealing the existence of multiple equilibria and immune system-dependent transitions","authors":"Jhoana P. Romero-Leiton , Alissen Peterson , Pablo Aguirre , Carlos Bastidas-Caldes , Bouchra Nasri","doi":"10.1016/j.chaos.2024.115912","DOIUrl":"10.1016/j.chaos.2024.115912","url":null,"abstract":"<div><div>The surge in antimicrobial resistance (AMR) is a critical global public health concern that complicates the eradication of harmful microorganisms within the host. Therefore, mathematical models have enhanced our understanding of AMR dynamics and aided in identifying measures to combat bacterial diseases, primarily focusing on single bacterial strains rather than microbial consortia. However, microbial consortia have not been extensively investigated. This study is a significant effort to examine the transmission of resistance in microbial communities, with a special focus on the ecological dynamics of microbial competition and the role of the host immune system in eradicating infections. We propose a mathematical model of AMR propagation that considers competition between two bacterial strains of the same species. Our analysis focuses on stability studies and the existence of bifurcations using different parameter values to represent the rate at which the host immune system eliminates bacteria. Our findings revealed that AMR propagation is primarily influenced by bacterial replication rate and host immune system efficacy. We observed that bacteria with lower replication rates could be effectively controlled, leading to disease extinction, whereas those with higher replication rates required a significantly robust immune response for clearance. The model demonstrated the existence of nine biologically feasible equilibrium points, with four explicitly associated with the different types of host immune systems characterized in the literature. Therefore, our study highlights the interplay between bacterial competition, immune system effectiveness, and AMR spread. We emphasize the importance of maintaining a robust immune system and establishing sensible antibiotic usage guidelines to slow the development and spread of antibiotic resistance.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115912"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887285","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115875
Sougata Mandal , Subhankar Sil , Sukhendu Ghosh
The study presents symmetry classifications of the linearized Navier–Stokes equations, governing the three-dimensional incompressible plane shear flows. The linearization is done with respect to small perturbations. In the case of a two-dimensional shear flow with a linear profile, Nold and Oberlack (PoF, 2013) showed the existence of three different kinds of linear instability modes using the framework of Lie symmetry classification. Those perturbation modes are normal mode, kelvin mode, and a new type invariant mode. We have extended their analysis for a three-dimensional plane shear flow with linear as well as non-linear base profiles. The invariant ansatz functions are systematically derived employing the full set of symmetries. The analysis is done for both viscous and inviscid flows by considering the linear, exponential, and fractional shear flow profiles. In the derivation process, the set of infinitesimal generators for the generalized system is first obtained using the classical Lie symmetry analysis, and then, some additional symmetries are searched out for each sub-case. Further, the governing system of partial differential equations is converted into ordinary differential equations by using symmetries and invariant conditions. The most popular three-dimensional normal modes and the Orr–Sommerfeld equation are acquired by taking the general symmetry. Moreover, for each of the sub-cases, we have derived the possible exact solutions of the associated system, and the behaviors of the solutions are explored for different parameter ranges.
{"title":"On the Lie symmetry analysis of three-dimensional perturbed shear flows","authors":"Sougata Mandal , Subhankar Sil , Sukhendu Ghosh","doi":"10.1016/j.chaos.2024.115875","DOIUrl":"10.1016/j.chaos.2024.115875","url":null,"abstract":"<div><div>The study presents symmetry classifications of the linearized Navier–Stokes equations, governing the three-dimensional incompressible plane shear flows. The linearization is done with respect to small perturbations. In the case of a two-dimensional shear flow with a linear profile, Nold and Oberlack (PoF, 2013) showed the existence of three different kinds of linear instability modes using the framework of Lie symmetry classification. Those perturbation modes are normal mode, kelvin mode, and a new type invariant mode. We have extended their analysis for a three-dimensional plane shear flow with linear as well as non-linear base profiles. The invariant ansatz functions are systematically derived employing the full set of symmetries. The analysis is done for both viscous and inviscid flows by considering the linear, exponential, and fractional shear flow profiles. In the derivation process, the set of infinitesimal generators for the generalized system is first obtained using the classical Lie symmetry analysis, and then, some additional symmetries are searched out for each sub-case. Further, the governing system of partial differential equations is converted into ordinary differential equations by using symmetries and invariant conditions. The most popular three-dimensional normal modes and the Orr–Sommerfeld equation are acquired by taking the general symmetry. Moreover, for each of the sub-cases, we have derived the possible exact solutions of the associated system, and the behaviors of the solutions are explored for different parameter ranges.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115875"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142815843","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 : 2025-02-01DOI: 10.1016/j.chaos.2024.115872
Karam Allali
This research paper examines the chaos control in porous media convection by imposing an external excitation on the system. The excitation is under the form of a quasi-periodic gravitational modulation with two incommensurate frequencies and . This will be accomplished by taking into consideration a two-dimensional rectangular porous layer that is saturated with fluid, heated from below, and subjected to a quasi-periodic vertical gravitational modulation. The model consists of a nonlinear heat equation coupled with a system of equations representing motion under the Darcy–Brinkman law. Utilizing a spectral approach, the problem is simplified into a set of four ordinary differential equations. Three equilibria of the system are given, namely the motionless convection steady state and convection steady states. The local and global stability for the motionless convection steady state were performed. Additionally, the local stability of the other equilibria is fulfilled. The fourth-order Runge–Kutta method is used to solve the system numerically. Numerical simulations have shown that the quasi-periodic gravitational modulation plays an essential role on the fluid dynamics behavior. We find chaotic and oscillating convection regimes depending on the ratio of gravitational modulation frequencies. It was demonstrated that by properly adjusting the frequencies ratio , transition from oscillating regime to chaos is observed and vice versa. Those transitions were checked by Poincaré section, Lyapunov exponent or phase diagram. It was concluded that controlling the dynamical behavior of the fluid in porous media may be achieved by implementing an appropriate quasi-periodic gravitational modulation.
{"title":"Oscillatory regimes and transition to chaos in a Darcy–Brinkman model under quasi-periodic gravitational modulation","authors":"Karam Allali","doi":"10.1016/j.chaos.2024.115872","DOIUrl":"10.1016/j.chaos.2024.115872","url":null,"abstract":"<div><div>This research paper examines the chaos control in porous media convection by imposing an external excitation on the system. The excitation is under the form of a quasi-periodic gravitational modulation with two incommensurate frequencies <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. This will be accomplished by taking into consideration a two-dimensional rectangular porous layer that is saturated with fluid, heated from below, and subjected to a quasi-periodic vertical gravitational modulation. The model consists of a nonlinear heat equation coupled with a system of equations representing motion under the Darcy–Brinkman law. Utilizing a spectral approach, the problem is simplified into a set of four ordinary differential equations. Three equilibria of the system are given, namely the motionless convection steady state and convection steady states. The local and global stability for the motionless convection steady state were performed. Additionally, the local stability of the other equilibria is fulfilled. The fourth-order Runge–Kutta method is used to solve the system numerically. Numerical simulations have shown that the quasi-periodic gravitational modulation plays an essential role on the fluid dynamics behavior. We find chaotic and oscillating convection regimes depending on the ratio of gravitational modulation frequencies. It was demonstrated that by properly adjusting the frequencies ratio <span><math><mrow><mi>η</mi><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>, transition from oscillating regime to chaos is observed and vice versa. Those transitions were checked by Poincaré section, Lyapunov exponent or phase diagram. It was concluded that controlling the dynamical behavior of the fluid in porous media may be achieved by implementing an appropriate quasi-periodic gravitational modulation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115872"},"PeriodicalIF":5.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857706","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}
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