Pub Date : 2025-01-25DOI: 10.1016/j.matcom.2025.01.016
Néstor García-Chan , Lino J. Alvarez-Vázquez , Aurea Martínez , Miguel E. Vázquez-Méndez
In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous media, respectively. Moreover, based in the interchange of mass in the porous media models, we can model the interchange of cars between streets and off-street parking-spaces. Therefore, our model is not a standard conservation law, being formulated as the coupling of a non-stationary convection–diffusion–reaction PDE with a Darcy–Brinkman–Forchheimer PDE system. To solve this model, the classical Galerkin finite element method combined with an explicit time marching scheme of strong stability preserving type was enough to stabilize our numerical solutions. Numerical experiences on an urban-porous domain inspired by the city of Guadalajara (Mexico) allow us to simulate the influence of the porosity terms on the traffic speed, the traffic flow at rush-valley hours, and traffic congestion due to the lack of parking spaces.
{"title":"A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city","authors":"Néstor García-Chan , Lino J. Alvarez-Vázquez , Aurea Martínez , Miguel E. Vázquez-Méndez","doi":"10.1016/j.matcom.2025.01.016","DOIUrl":"10.1016/j.matcom.2025.01.016","url":null,"abstract":"<div><div>In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous media, respectively. Moreover, based in the interchange of mass in the porous media models, we can model the interchange of cars between streets and off-street parking-spaces. Therefore, our model is not a standard conservation law, being formulated as the coupling of a non-stationary convection–diffusion–reaction PDE with a Darcy–Brinkman–Forchheimer PDE system. To solve this model, the classical Galerkin <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> finite element method combined with an explicit time marching scheme of strong stability preserving type was enough to stabilize our numerical solutions. Numerical experiences on an urban-porous domain inspired by the city of Guadalajara (Mexico) allow us to simulate the influence of the porosity terms on the traffic speed, the traffic flow at rush-valley hours, and traffic congestion due to the lack of parking spaces.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 60-74"},"PeriodicalIF":4.4,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143226664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-23DOI: 10.1016/j.matcom.2025.01.013
Soham Shanbhag, Dong Eui Chang
The estimate of a system state, arrived at using measurements, is often used in design of state controllers in robotics. These measurements are often biased and contain noise. Many such systems usually evolve on matrix Lie groups. In this paper, we propose a globally exponentially convergent observer for systems evolving on matrix Lie groups with bounded velocity. The design of observers on the Lie group prohibits continuous globally convergent observers, which we sidestep by designing the observer in the ambient Euclidean space of the group and show exponential convergence of the observer to the state of the system. The performance of the observer is shown using an example of the rigid body rotation and translation system evolving on the special Euclidean group. We also compare the proposed observer with an observer present in the literature and show the improvements afforded by our observer.
{"title":"Globally exponentially convergent observer for systems evolving on matrix Lie groups","authors":"Soham Shanbhag, Dong Eui Chang","doi":"10.1016/j.matcom.2025.01.013","DOIUrl":"10.1016/j.matcom.2025.01.013","url":null,"abstract":"<div><div>The estimate of a system state, arrived at using measurements, is often used in design of state controllers in robotics. These measurements are often biased and contain noise. Many such systems usually evolve on matrix Lie groups. In this paper, we propose a globally exponentially convergent observer for systems evolving on matrix Lie groups with bounded velocity. The design of observers on the Lie group prohibits continuous globally convergent observers, which we sidestep by designing the observer in the ambient Euclidean space of the group and show exponential convergence of the observer to the state of the system. The performance of the observer is shown using an example of the rigid body rotation and translation system evolving on the special Euclidean group. We also compare the proposed observer with an observer present in the literature and show the improvements afforded by our observer.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 475-482"},"PeriodicalIF":4.4,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-20DOI: 10.1016/j.matcom.2025.01.015
Xin Chen, Zeyu Zhang, Peiqi Huang
This paper investigates linear quadratic (LQ) optimal control problems of forward uncertain and backward stochastic multi-stage systems. First, leveraging dynamic programming, we derive stochastic recursive equations tailored to address an LQ optimal control problem for backward stochastic multi-stage systems within a probabilistic framework. Subsequently, we extend our analysis to an equivalent LQ optimal control problem formulated under chance theory, incorporating both forward uncertain and backward stochastic dynamics. From this, we derive uncertain stochastic recursive equations to solve the equivalent problem and provide explicit analytical expressions for the optimal control strategies and corresponding optimal values. Additionally, we explore the effects of variable separability within uncertain random variables, demonstrating that under chance theory, the optimal solutions of LQ optimal control problems remain consistent when uncertain and random variables are separable. Finally, a numerical example is provided to validate our results.
{"title":"Uncertain stochastic linear quadratic control subject to forward and backward multi-stage systems","authors":"Xin Chen, Zeyu Zhang, Peiqi Huang","doi":"10.1016/j.matcom.2025.01.015","DOIUrl":"10.1016/j.matcom.2025.01.015","url":null,"abstract":"<div><div>This paper investigates linear quadratic (LQ) optimal control problems of forward uncertain and backward stochastic multi-stage systems. First, leveraging dynamic programming, we derive stochastic recursive equations tailored to address an LQ optimal control problem for backward stochastic multi-stage systems within a probabilistic framework. Subsequently, we extend our analysis to an equivalent LQ optimal control problem formulated under chance theory, incorporating both forward uncertain and backward stochastic dynamics. From this, we derive uncertain stochastic recursive equations to solve the equivalent problem and provide explicit analytical expressions for the optimal control strategies and corresponding optimal values. Additionally, we explore the effects of variable separability within uncertain random variables, demonstrating that under chance theory, the optimal solutions of LQ optimal control problems remain consistent when uncertain and random variables are separable. Finally, a numerical example is provided to validate our results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 1-20"},"PeriodicalIF":4.4,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143226045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-18DOI: 10.1016/j.matcom.2025.01.014
Dingding Cao, Changpin Li
In this study, the analysis and computation for quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem is investigated. Initial findings confirm that its classical solution exhibits non-negativity and quenching in a finite time. Then the numerical method is established to detect the quenching phenomenon in the considered problem. Numerical simulations are provided to show the effectiveness of the theoretical analysis and computation.
{"title":"Quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem: Analysis and computation","authors":"Dingding Cao, Changpin Li","doi":"10.1016/j.matcom.2025.01.014","DOIUrl":"10.1016/j.matcom.2025.01.014","url":null,"abstract":"<div><div>In this study, the analysis and computation for quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem is investigated. Initial findings confirm that its classical solution exhibits non-negativity and quenching in a finite time. Then the numerical method is established to detect the quenching phenomenon in the considered problem. Numerical simulations are provided to show the effectiveness of the theoretical analysis and computation.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 21-38"},"PeriodicalIF":4.4,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143226046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-17DOI: 10.1016/j.matcom.2025.01.012
Marc Vidal , Ana M. Aguilera
We address the mathematical and statistical formalism that underpins optimal estimation of brain activity in artifact-corrupted electroencephalographic (EEG) signals. We argue the reconstruction of artifacts relates to approximating a function in a Hilbert basis that is a realization of a spatio-temporal random variable taking values in a Hilbert space. A model for sparse optimization based on a fixed-point iteration over the spatial domain and posterior enhancement in the temporal domain via wavelet thresholding is discussed under the paradigm of “wide functional data”. Two criteria are introduced for selecting wavelet expansion coefficients in scenarios where noise lacks a precise parametric specification: one based on multiplicative scaling and the other on the entropic NID (ENID), as introduced in Bruni et al. (2020). Through comprehensive numerical simulations and real data analyses of EEG data, we showcase the effectiveness of the proposed methods.
{"title":"Wavelet thresholding on independent subspace factorizations of spatially indexed wide functional data for robust estimation of cortical activity","authors":"Marc Vidal , Ana M. Aguilera","doi":"10.1016/j.matcom.2025.01.012","DOIUrl":"10.1016/j.matcom.2025.01.012","url":null,"abstract":"<div><div>We address the mathematical and statistical formalism that underpins optimal estimation of brain activity in artifact-corrupted electroencephalographic (EEG) signals. We argue the reconstruction of artifacts relates to approximating a function in a Hilbert basis that is a realization of a spatio-temporal random variable taking values in a Hilbert space. A model for sparse optimization based on a fixed-point iteration over the spatial domain and posterior enhancement in the temporal domain via wavelet thresholding is discussed under the paradigm of “wide functional data”. Two criteria are introduced for selecting wavelet expansion coefficients in scenarios where noise lacks a precise parametric specification: one based on multiplicative scaling and the other on the entropic NID (ENID), as introduced in Bruni et al. (2020). Through comprehensive numerical simulations and real data analyses of EEG data, we showcase the effectiveness of the proposed methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 346-361"},"PeriodicalIF":4.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-17DOI: 10.1016/j.matcom.2025.01.011
Yong Zhang
Image information security is a hot research area in cryptography after text encryption research. To effectively secure digital images, a practical and graceful new image encryption algorithm was proposed in this paper. Firstly, four substitution boxes (S-boxes) are constructed based on the method of generating S-box of AES. Secondly, a chaotic system with uniform probability density function is created by fusing piecewise linear map (PWLM) and Arnold cat map. The resulting system is used to produce an equivalent-key sequence of the same size as the plain image using an external secret key of length 256 bits. Thirdly, a butterfly encoding module based on the butterfly node algorithm is presented. Finally, the basic image cryptosystem based on the butterfly encoding module, the enhanced image cryptosystem with cipher-text sensitivity, and the unified image cryptosystem with identical encryption and decryption processes are sequentially studied. The performance analysis shows that the proposed image encryption systems have a time complexity of 3 and a spatial complexity of approximately 3.03, the generated cipher images are similar to noise images, and the secret key, the equivalent key, and the plain image are all extremely sensitive. Thus, the proposed cryptographies are high-speed and secure image encryption algorithms.
{"title":"Image encryption algorithm based on butterfly module and chaos","authors":"Yong Zhang","doi":"10.1016/j.matcom.2025.01.011","DOIUrl":"10.1016/j.matcom.2025.01.011","url":null,"abstract":"<div><div>Image information security is a hot research area in cryptography after text encryption research. To effectively secure digital images, a practical and graceful new image encryption algorithm was proposed in this paper. Firstly, four substitution boxes (S-boxes) are constructed based on the method of generating S-box of AES. Secondly, a chaotic system with uniform probability density function is created by fusing piecewise linear map (PWLM) and Arnold cat map. The resulting system is used to produce an equivalent-key sequence of the same size as the plain image using an external secret key of length 256 bits. Thirdly, a butterfly encoding module based on the butterfly node algorithm is presented. Finally, the basic image cryptosystem based on the butterfly encoding module, the enhanced image cryptosystem with cipher-text sensitivity, and the unified image cryptosystem with identical encryption and decryption processes are sequentially studied. The performance analysis shows that the proposed image encryption systems have a time complexity of 3 and a spatial complexity of approximately 3.03, the generated cipher images are similar to noise images, and the secret key, the equivalent key, and the plain image are all extremely sensitive. Thus, the proposed cryptographies are high-speed and secure image encryption algorithms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 382-407"},"PeriodicalIF":4.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-17DOI: 10.1016/j.matcom.2025.01.009
Said Ounamane , Lakhlifa Sadek , Bouchra Abouzaid , El Mostafa Sadek
In this paper, we employ the Caputo fractional derivative (CFD) approach and utilize the truncated exponential method to tackle linear fractional optimal control problems (FOCPs) with equality and inequality constraints in multi-dimensional settings. By applying the truncated exponential method, we transform the FOCP into a system of algebraic equations that can be readily solved. Our analysis extends to the convergence and error estimation (EE) of truncated exponential method polynomials, and we introduce a residual correction procedure to refine error estimates. To assess the effectiveness and applicability of the proposed method, we conduct experiments on three different examples and compare our results with those of the previously obtained ones. Our findings yield very satisfactory results, and in some cases, we obtain exact solutions.
{"title":"Fractional truncated exponential method for linear fractional optimal control problems","authors":"Said Ounamane , Lakhlifa Sadek , Bouchra Abouzaid , El Mostafa Sadek","doi":"10.1016/j.matcom.2025.01.009","DOIUrl":"10.1016/j.matcom.2025.01.009","url":null,"abstract":"<div><div>In this paper, we employ the Caputo fractional derivative (CFD) approach and utilize the truncated exponential method to tackle linear fractional optimal control problems (FOCPs) with equality and inequality constraints in multi-dimensional settings. By applying the truncated exponential method, we transform the FOCP into a system of algebraic equations that can be readily solved. Our analysis extends to the convergence and error estimation (EE) of truncated exponential method polynomials, and we introduce a residual correction procedure to refine error estimates. To assess the effectiveness and applicability of the proposed method, we conduct experiments on three different examples and compare our results with those of the previously obtained ones. Our findings yield very satisfactory results, and in some cases, we obtain exact solutions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 408-426"},"PeriodicalIF":4.4,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-16DOI: 10.1016/j.matcom.2025.01.007
Hongyang Zhang , Shuting Wang , Yuanlong Xie , Hu Li , Shiqi Zheng
Dynamic selection of representative operators shows great promise for multi-objective optimization, but existing methods suffer from difficulties in balancing fair comparison of operators with dynamic adaptation of evolutionary states, and inaccurate evaluation of operator quality. This paper proposes a leadership succession inspired adaptive operator selection mechanism (LS-AOS), aiming to enhance dynamic matching with time-varying evolutionary states while ensuring fair operator comparisons. In LS-AOS, a new campaign-incumbency rule is designed to be implemented iteratively to allow operators to undergo a fair campaign process, thus identifying optimal operators for generating offspring. Additionally, a two-layer oversight strategy is proposed to make real-time adjustments to operator selection and pool configuration based on operator performance and evolutionary state, with the aim of satisfying the diverse requirements for exploration and exploitation during the evolutionary process. To refine and improve the evaluation of operator quality, the novel Election Campaign Indicator (ECI) is designed that uniquely integrates measures of population diversity and convergence, and effectively extends the applicability of LS-AOS. The experimental results on 23 test problems indicate that LS-AOS possesses feasibility and can effectively improve the performance of benchmark algorithms. Compared with the existing state-of-the-art algorithms, the proposed LS-AOS exhibits sufficient competitiveness and advancement.
{"title":"Leadership succession inspired adaptive operator selection mechanism for multi-objective optimization","authors":"Hongyang Zhang , Shuting Wang , Yuanlong Xie , Hu Li , Shiqi Zheng","doi":"10.1016/j.matcom.2025.01.007","DOIUrl":"10.1016/j.matcom.2025.01.007","url":null,"abstract":"<div><div>Dynamic selection of representative operators shows great promise for multi-objective optimization, but existing methods suffer from difficulties in balancing fair comparison of operators with dynamic adaptation of evolutionary states, and inaccurate evaluation of operator quality. This paper proposes a leadership succession inspired adaptive operator selection mechanism (LS-AOS), aiming to enhance dynamic matching with time-varying evolutionary states while ensuring fair operator comparisons. In LS-AOS, a new campaign-incumbency rule is designed to be implemented iteratively to allow operators to undergo a fair campaign process, thus identifying optimal operators for generating offspring. Additionally, a two-layer oversight strategy is proposed to make real-time adjustments to operator selection and pool configuration based on operator performance and evolutionary state, with the aim of satisfying the diverse requirements for exploration and exploitation during the evolutionary process. To refine and improve the evaluation of operator quality, the novel Election Campaign Indicator (<em>ECI</em>) is designed that uniquely integrates measures of population diversity and convergence, and effectively extends the applicability of LS-AOS. The experimental results on 23 test problems indicate that LS-AOS possesses feasibility and can effectively improve the performance of benchmark algorithms. Compared with the existing state-of-the-art algorithms, the proposed LS-AOS exhibits sufficient competitiveness and advancement.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 454-474"},"PeriodicalIF":4.4,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-14DOI: 10.1016/j.matcom.2025.01.010
Hai Zhang , Panqing Gao , Renyu Ye , Ivanka Stamova , Jinde Cao
The fixed time synchronization (Fix-TS) and predefined time synchronization (Pre-TS) of fractional quaternion delayed neural networks (FQDNNs) with disturbances using fractional sliding mode (FSM) control are investigated. We first introduce an enhanced lemma for fixed time (Fix-T) and predefined time (Pre-T) stability, expanding upon the existing stability theory. Subsequently, we introduce the FQDNNs model with disturbance terms, which is less conservative. By constructing two FSM controllers, we derive several theorems for Fix-TS and Pre-TS, respectively. The concise criterion and accurate setting time are demonstrated through numerical simulations, and graphic visualization directly verifies the results.
{"title":"Fixed/Predefined time synchronization of fractional quaternion delayed neural networks with disturbances","authors":"Hai Zhang , Panqing Gao , Renyu Ye , Ivanka Stamova , Jinde Cao","doi":"10.1016/j.matcom.2025.01.010","DOIUrl":"10.1016/j.matcom.2025.01.010","url":null,"abstract":"<div><div>The fixed time synchronization (Fix-TS) and predefined time synchronization (Pre-TS) of fractional quaternion delayed neural networks (FQDNNs) with disturbances using fractional sliding mode (FSM) control are investigated. We first introduce an enhanced lemma for fixed time (Fix-T) and predefined time (Pre-T) stability, expanding upon the existing stability theory. Subsequently, we introduce the FQDNNs model with disturbance terms, which is less conservative. By constructing two FSM controllers, we derive several theorems for Fix-TS and Pre-TS, respectively. The concise criterion and accurate setting time are demonstrated through numerical simulations, and graphic visualization directly verifies the results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 276-294"},"PeriodicalIF":4.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-14DOI: 10.1016/j.matcom.2025.01.004
Jyotsna Kumari Bharti , K. Murugesan , P. Balasubramaniam
External disturbance, uncertainty and time delay are basic ideas of nonlinear systems that are highly related to the control and synchronization of nonlinear systems. This paper introduces a novel approach for achieving synchronization in non-identical chaotic systems in the presence of model uncertainty, external disturbances and time delay. The proposed method utilizes a matrix projective combination synchronization strategy, demonstrating its efficacy in scenarios both with and without time delay. Notably, the application of this strategy has proven to be valuable and efficient, particularly in the domain of encrypting images. This work proceeds by combining two drive systems and one response system using Lyapunov stability theory and a suitable active control technique. Numerical examples are taken to verify the effectiveness of the proposed method and numerical simulations have been performed to demonstrate that the theoretical results are completely consistent with the graphical results. A significant idea for encryption and decryption algorithms is that the secure transmission of images using affine encryption. In affine encryption algorithm, the key is based on the solution of synchronized chaotic delayed disturbed systems and the birth date and birth time of the sender and receiver. The proposed encryption and decryption algorithms have been applied to plain images. Their effectiveness has been validated through key security metrics. Additionally, a comparative analysis with previously published methods demonstrates the robustness and efficiency of the approach.
{"title":"Matrix projective combination synchronization of time-delayed chaotic system and its application in image encryption","authors":"Jyotsna Kumari Bharti , K. Murugesan , P. Balasubramaniam","doi":"10.1016/j.matcom.2025.01.004","DOIUrl":"10.1016/j.matcom.2025.01.004","url":null,"abstract":"<div><div>External disturbance, uncertainty and time delay are basic ideas of nonlinear systems that are highly related to the control and synchronization of nonlinear systems. This paper introduces a novel approach for achieving synchronization in non-identical chaotic systems in the presence of model uncertainty, external disturbances and time delay. The proposed method utilizes a matrix projective combination synchronization strategy, demonstrating its efficacy in scenarios both with and without time delay. Notably, the application of this strategy has proven to be valuable and efficient, particularly in the domain of encrypting images. This work proceeds by combining two drive systems and one response system using Lyapunov stability theory and a suitable active control technique. Numerical examples are taken to verify the effectiveness of the proposed method and numerical simulations have been performed to demonstrate that the theoretical results are completely consistent with the graphical results. A significant idea for encryption and decryption algorithms is that the secure transmission of images using affine encryption. In affine encryption algorithm, the key is based on the solution of synchronized chaotic delayed disturbed systems and the birth date and birth time of the sender and receiver. The proposed encryption and decryption algorithms have been applied to plain images. Their effectiveness has been validated through key security metrics. Additionally, a comparative analysis with previously published methods demonstrates the robustness and efficiency of the approach.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 311-345"},"PeriodicalIF":4.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号