Pub Date : 2024-10-09DOI: 10.1016/j.amc.2024.129093
Saloni Gupta, Arnab Kayal, Moumita Mandal
In this article, we propose Chebyshev spectral projection methods to solve the hypersingular integral equation of first kind. The presence of strong singularity in Hadamard sense in the first part of the integral equation makes it challenging to get superconvergence results. To overcome this, we transform the first kind hypersingular integral equation into a second kind integral equation. This is achieved by defining a bounded inverse of the hypersingular integral operator in some suitable Hilbert space. Using iterated Chebyshev spectral Galerkin method on the equivalent second kind integral equation, we obtain improved convergence of , where is the highest degree of Chebyshev polynomials employed in the approximation space and r is the smoothness of the solution. Further, using commutativity of projection operator and inverse of the hypersingular integral operator, we are able to obtain superconvergence of and , by Chebyshev spectral multi-Galerkin method (CSMGM) and iterated CSMGM, respectively. Finally, numerical examples are presented to verify our theoretical results.
{"title":"Superconvergence results for hypersingular integral equation of first kind by Chebyshev spectral projection methods","authors":"Saloni Gupta, Arnab Kayal, Moumita Mandal","doi":"10.1016/j.amc.2024.129093","DOIUrl":"10.1016/j.amc.2024.129093","url":null,"abstract":"<div><div>In this article, we propose Chebyshev spectral projection methods to solve the hypersingular integral equation of first kind. The presence of strong singularity in Hadamard sense in the first part of the integral equation makes it challenging to get superconvergence results. To overcome this, we transform the first kind hypersingular integral equation into a second kind integral equation. This is achieved by defining a bounded inverse of the hypersingular integral operator in some suitable Hilbert space. Using iterated Chebyshev spectral Galerkin method on the equivalent second kind integral equation, we obtain improved convergence of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>N</mi></math></span> is the highest degree of Chebyshev polynomials employed in the approximation space and <em>r</em> is the smoothness of the solution. Further, using commutativity of projection operator and inverse of the hypersingular integral operator, we are able to obtain superconvergence of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>3</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>4</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span>, by Chebyshev spectral multi-Galerkin method (CSMGM) and iterated CSMGM, respectively. Finally, numerical examples are presented to verify our theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129093"},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421529","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 : 2024-10-09DOI: 10.1016/j.amc.2024.129091
Andreas Meier, Eberhard Bänsch, Florian Frank
We couple the momentum and mass balance equations with the bead-rod chain model (Kramers chain) to simulate non-Newtonian polymeric fluids using finite elements and the Brownian configuration field method. A suitable rod-length preserving discretization is presented, which is based on the ideas of Liu's algorithm [28] and generalized into the finite-element context. Additional details concerning the parallelization of the Brownian configuration field part of the simulation are discussed to achieve outstanding code runtimes on large computation clusters. The novel coupling enables the investigation of how the bead-rod chains influence the fluid flow. This is done with proof-of-concept simulations for the start-up shear flow and flow around a cylinder scenario in 2D that serve as a reference for future research. In the start-up shear flow scenario, the velocity overshoot effect, which is typical for polymeric fluids, is successfully demonstrated. In the more challenging flow around a cylinder scenario, we numerically confirm the viscoelastic drag reduction phenomenon by comparing the drag coefficients with a purely Newtonian Navier–Stokes solution.
{"title":"Multiscale flow simulations of dilute polymeric solutions with bead-rod chains using Brownian configuration fields","authors":"Andreas Meier, Eberhard Bänsch, Florian Frank","doi":"10.1016/j.amc.2024.129091","DOIUrl":"10.1016/j.amc.2024.129091","url":null,"abstract":"<div><div>We couple the momentum and mass balance equations with the bead-rod chain model (Kramers chain) to simulate non-Newtonian polymeric fluids using finite elements and the Brownian configuration field method. A suitable rod-length preserving discretization is presented, which is based on the ideas of Liu's algorithm <span><span>[28]</span></span> and generalized into the finite-element context. Additional details concerning the parallelization of the Brownian configuration field part of the simulation are discussed to achieve outstanding code runtimes on large computation clusters. The novel coupling enables the investigation of how the bead-rod chains influence the fluid flow. This is done with proof-of-concept simulations for the start-up shear flow and flow around a cylinder scenario in 2D that serve as a reference for future research. In the start-up shear flow scenario, the velocity overshoot effect, which is typical for polymeric fluids, is successfully demonstrated. In the more challenging flow around a cylinder scenario, we numerically confirm the viscoelastic drag reduction phenomenon by comparing the drag coefficients with a purely Newtonian Navier–Stokes solution.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129091"},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.amc.2024.129092
André J.P. de Oliveira , Diego C. Knupp , Luiz A.S. Abreu
In many engineering problems non-linear mathematical models are needed to accurately describe the physical phenomena involved. In such cases, the inverse problems related to those models bring additional challenges. In this scenario, this work provides a novel general regularized methodology based on integral transforms for obtaining explicit solutions to inverse problems related to source term estimation in non-linear advection-diffusion models. Numerical examples demonstrate the application of the methodology for some cases of the one- and two-dimensional versions of the non-linear Burgers' equation. An uncertainty analysis for the proposed inverse problem is also conducted using the Monte Carlo Method, in order to illustrate the reliability of the estimates. The results reveal accurate estimates for different functional forms of the sought source term and varying noise levels, for both diffusion-dominated and advection-dominated scenarios.
{"title":"Integral transforms for explicit source estimation in non-linear advection-diffusion problems","authors":"André J.P. de Oliveira , Diego C. Knupp , Luiz A.S. Abreu","doi":"10.1016/j.amc.2024.129092","DOIUrl":"10.1016/j.amc.2024.129092","url":null,"abstract":"<div><div>In many engineering problems non-linear mathematical models are needed to accurately describe the physical phenomena involved. In such cases, the inverse problems related to those models bring additional challenges. In this scenario, this work provides a novel general regularized methodology based on integral transforms for obtaining explicit solutions to inverse problems related to source term estimation in non-linear advection-diffusion models. Numerical examples demonstrate the application of the methodology for some cases of the one- and two-dimensional versions of the non-linear Burgers' equation. An uncertainty analysis for the proposed inverse problem is also conducted using the Monte Carlo Method, in order to illustrate the reliability of the estimates. The results reveal accurate estimates for different functional forms of the sought source term and varying noise levels, for both diffusion-dominated and advection-dominated scenarios.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129092"},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421530","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 : 2024-10-09DOI: 10.1016/j.amc.2024.129088
Hassan Askari, Alireza Ansari
In this paper, using the higher-order differential equation of M-Wright function (Mainardi function) of order , we get the integral representations for this function and other linear independent functions on the Laplace contours. The Stokes phenomenon and the Stokes/anti-Stokes rays for different domains in the complex plane are also investigated. Our approach is based on the steepest descent method for analyzing and drawing the steepest descent curves/directions for the initial values of n.
本文利用阶数为 1n,n≥3 的 M-赖特函数（Mainardi 函数）的高阶微分方程，得到了该函数和其他线性独立函数在拉普拉斯等值线上的积分表示。我们还研究了复平面内不同域的斯托克斯现象和斯托克斯/反斯托克斯射线。我们的方法基于最陡下降法，用于分析和绘制 n 初始值的最陡下降曲线/方向。
{"title":"Stokes phenomenon for the M-Wright function of order 1n","authors":"Hassan Askari, Alireza Ansari","doi":"10.1016/j.amc.2024.129088","DOIUrl":"10.1016/j.amc.2024.129088","url":null,"abstract":"<div><div>In this paper, using the higher-order differential equation of M-Wright function (Mainardi function) of order <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>,</mo><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, we get the integral representations for this function and other linear independent functions on the Laplace contours. The Stokes phenomenon and the Stokes/anti-Stokes rays for different domains in the complex plane are also investigated. Our approach is based on the steepest descent method for analyzing and drawing the steepest descent curves/directions for the initial values of <em>n</em>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129088"},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421867","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 : 2024-10-08DOI: 10.1016/j.amc.2024.129112
Indra Bate, Kedarnath Senapati, Santhosh George, Muniyasamy M, Chandhini G
In this paper, we study the local convergence analysis of the Jarratt-type iterative methods for solving non-linear equations in the Banach space setting without using the Taylor expansion. Convergence analysis using Taylor series required the operator to be differentiable at least times, where p is the order of convergence. In our convergence analysis, we do not use the Taylor expansion, so we require only assumptions on the derivatives of the involved operator of order up to three only. Thus, we extended the applicability of the methods under study. Further, we obtained a six-order Jarratt-type method by utilising the method studied by Hueso et al. in 2015. Numerical examples and dynamics of the methods are presented to illustrate the theoretical results.
{"title":"Jarratt-type methods and their convergence analysis without using Taylor expansion","authors":"Indra Bate, Kedarnath Senapati, Santhosh George, Muniyasamy M, Chandhini G","doi":"10.1016/j.amc.2024.129112","DOIUrl":"10.1016/j.amc.2024.129112","url":null,"abstract":"<div><div>In this paper, we study the local convergence analysis of the Jarratt-type iterative methods for solving non-linear equations in the Banach space setting without using the Taylor expansion. Convergence analysis using Taylor series required the operator to be differentiable at least <span><math><mi>p</mi><mo>+</mo><mn>1</mn></math></span> times, where <em>p</em> is the order of convergence. In our convergence analysis, we do not use the Taylor expansion, so we require only assumptions on the derivatives of the involved operator of order up to three only. Thus, we extended the applicability of the methods under study. Further, we obtained a six-order Jarratt-type method by utilising the method studied by Hueso et al. in 2015. Numerical examples and dynamics of the methods are presented to illustrate the theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129112"},"PeriodicalIF":3.5,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421871","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 : 2024-10-08DOI: 10.1016/j.amc.2024.129113
Xiaofeng Chen , Dongyuan Lin , Hua Li , Zhi Cheng
High-order extend Kalman filtering (HEKF) is an excellent tool for addressing state estimation challenges in highly nonlinear systems under Gaussian noise conditions. However, HEKF may yield estimates with significant biases when the considered system is subjected to non-Gaussian disturbances. In response to this challenge, based on the minimum error entropy with fiducial points (MEEF), a novel HEKF (MEEFHEKF) is developed, and it exhibits robustness against intricate non-Gaussian noises. First, the nonlinear system is transformed into an augmented linear model through high-order Taylor approximation techniques. Subsequently, the development of the MEEFHEKF ensues through the resolution of an optimization problem grounded in the MEEF within the context of an augmented linear model. The MEEFHEKF, as put forward, operates as an online algorithm adopting a recursive structure, wherein the iterative equation is utilized to update the posterior estimates. Moreover, a sufficient condition is presented to confirm the existence and uniqueness of the fixed point in the iteration equation, guaranteeing the convergence of the introduced MEEFHEKF. Furthermore, an analysis of its computational complexity is also conducted to illustrate the computational burden. Finally, simulations substantiate the elevated precision in filtering and formidable robustness exhibited by the proposed algorithms when confronted with non-Gaussian disturbances.
{"title":"Minimum error entropy high-order extend Kalman filter with fiducial points","authors":"Xiaofeng Chen , Dongyuan Lin , Hua Li , Zhi Cheng","doi":"10.1016/j.amc.2024.129113","DOIUrl":"10.1016/j.amc.2024.129113","url":null,"abstract":"<div><div>High-order extend Kalman filtering (HEKF) is an excellent tool for addressing state estimation challenges in highly nonlinear systems under Gaussian noise conditions. However, HEKF may yield estimates with significant biases when the considered system is subjected to non-Gaussian disturbances. In response to this challenge, based on the minimum error entropy with fiducial points (MEEF), a novel HEKF (MEEFHEKF) is developed, and it exhibits robustness against intricate non-Gaussian noises. First, the nonlinear system is transformed into an augmented linear model through high-order Taylor approximation techniques. Subsequently, the development of the MEEFHEKF ensues through the resolution of an optimization problem grounded in the MEEF within the context of an augmented linear model. The MEEFHEKF, as put forward, operates as an online algorithm adopting a recursive structure, wherein the iterative equation is utilized to update the posterior estimates. Moreover, a sufficient condition is presented to confirm the existence and uniqueness of the fixed point in the iteration equation, guaranteeing the convergence of the introduced MEEFHEKF. Furthermore, an analysis of its computational complexity is also conducted to illustrate the computational burden. Finally, simulations substantiate the elevated precision in filtering and formidable robustness exhibited by the proposed algorithms when confronted with non-Gaussian disturbances.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129113"},"PeriodicalIF":3.5,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421870","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 : 2024-10-07DOI: 10.1016/j.amc.2024.129082
Yusuf Bilfaqih, Mochamad Nur Qomarudin, Mochammad Sahal
System reliability analysis in discrete phase-type (DPH) distributions requires longer computation time as the matrix order increases with the number of components and the complexity of the system structure. This paper presents a method to reduce the computation time by performing a similarity transformation on the DPH distribution model of the component lifetimes. Similarity transformation produces a matrix-geometric (MG) distribution whose generator matrix is in Jordan canonical form with fewer non-zero elements, so the computation time is faster. We modified the algorithms for system reliability in DPH distributions to make them applicable to MG distributions. Our experiments using several Jordan canonical forms show significant reductions in computation times.
{"title":"Time-dependent reliability computation of system with multistate components","authors":"Yusuf Bilfaqih, Mochamad Nur Qomarudin, Mochammad Sahal","doi":"10.1016/j.amc.2024.129082","DOIUrl":"10.1016/j.amc.2024.129082","url":null,"abstract":"<div><div>System reliability analysis in discrete phase-type (DPH) distributions requires longer computation time as the matrix order increases with the number of components and the complexity of the system structure. This paper presents a method to reduce the computation time by performing a similarity transformation on the DPH distribution model of the component lifetimes. Similarity transformation produces a matrix-geometric (MG) distribution whose generator matrix is in Jordan canonical form with fewer non-zero elements, so the computation time is faster. We modified the algorithms for system reliability in DPH distributions to make them applicable to MG distributions. Our experiments using several Jordan canonical forms show significant reductions in computation times.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129082"},"PeriodicalIF":3.5,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421868","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}
To tackle the trajectory-following problem of multiple unmanned aerial vehicles (UAVs) characterized by high non-linearity and strong coupling, this paper methodologically separates the dynamics of fixed-wing UAVs into two subsystems and designs appropriate controllers for each loop. Unlike previous works, the proposed multi-purpose method simultaneously accounts for constraints, computational time, external disturbances, and actuator faults. The inclusive structure of the proposed strategy is as follows: Firstly, in the outer loop, by employing the high precision and constraint-handling attributes of nonlinear model predictive control (NMPC), the trajectories of the agents are guided to their reference positions while considering spatial limitations, including no-fly zone evasion and inter-vehicle collision evasion. Then, the optimal states of the inner loop are designed. Secondly, in the inner loop, a fault-tolerant sliding mode predictive control (SMPC) is reconfigured to accommodate identified actuator faults and follow the optimal states produced by NMPC. The effectiveness of the suggested algorithm is verified through a series of simulation results. Comparison simulation results substantiate the ascendancy of the suggested dual-loop method over the NMPC trajectory replanning algorithm.
{"title":"Fault-tolerant model predictive sliding mode control for trajectory replanning of multi-UAV formation flight","authors":"Maria Khodaverdian , Majdeddin Najafi , Omid Kazemifar , Shahabuddin Rahmanian","doi":"10.1016/j.amc.2024.129073","DOIUrl":"10.1016/j.amc.2024.129073","url":null,"abstract":"<div><div>To tackle the trajectory-following problem of multiple unmanned aerial vehicles (UAVs) characterized by high non-linearity and strong coupling, this paper methodologically separates the dynamics of fixed-wing UAVs into two subsystems and designs appropriate controllers for each loop. Unlike previous works, the proposed multi-purpose method simultaneously accounts for constraints, computational time, external disturbances, and actuator faults. The inclusive structure of the proposed strategy is as follows: Firstly, in the outer loop, by employing the high precision and constraint-handling attributes of nonlinear model predictive control (NMPC), the trajectories of the agents are guided to their reference positions while considering spatial limitations, including no-fly zone evasion and inter-vehicle collision evasion. Then, the optimal states of the inner loop are designed. Secondly, in the inner loop, a fault-tolerant sliding mode predictive control (SMPC) is reconfigured to accommodate identified actuator faults and follow the optimal states produced by NMPC. The effectiveness of the suggested algorithm is verified through a series of simulation results. Comparison simulation results substantiate the ascendancy of the suggested dual-loop method over the NMPC trajectory replanning algorithm.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129073"},"PeriodicalIF":3.5,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357171","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 : 2024-09-30DOI: 10.1016/j.amc.2024.129083
Yikang Lu , Hui Dai , Huaiyu Tan , Xiaofang Duan , Lei Shi , Junpyo Park
Higher-order interactions (HOIs) are ubiquitous in real systems, and HOIs among individuals complicate the exploration of species diversity for populations in ecosystems. Therefore, understanding how higher-order interactions affect biodiversity is essential but poses significant challenges. In this paper, we consider higher-order interactions in the competitive processes of spatial rock-paper-scissors (RPS) dynamics, specifically within spatially embedded hyper-lattices, and investigate what biodiversity can be driven by HOIs. Considering hyperedges, species in hyperedges can be different, and different relationships are considered, which can eventually demonstrate the strength of competition. With the competition intensity modulated by the sensitivity of HOIs, extensive simulations have shown that higher-order competitive processes can promote coexistence. We also found that stratification of species densities occurs when three species coexist due to HOIs, which are closely related to the increase of empty sites and disordered spiral entanglement. From investigating the extinction probability in a broad aspect, it has been found that, even if HOIs are working, the coexistence in the system is eventually broken at high mobility regimes. The intensified sensitivity to HOIs can somewhat alleviate extinction, although no striking change has occurred. Our findings may address that modeling predator-prey interactions incorporating HOIs is important for gaining insights into biodiversity, and we hope our study may provide a broad aspect for exploring complex ecosystems.
{"title":"Enhancement of persistence in the rock-paper-scissors dynamics through higher-order interactions","authors":"Yikang Lu , Hui Dai , Huaiyu Tan , Xiaofang Duan , Lei Shi , Junpyo Park","doi":"10.1016/j.amc.2024.129083","DOIUrl":"10.1016/j.amc.2024.129083","url":null,"abstract":"<div><div>Higher-order interactions (HOIs) are ubiquitous in real systems, and HOIs among individuals complicate the exploration of species diversity for populations in ecosystems. Therefore, understanding how higher-order interactions affect biodiversity is essential but poses significant challenges. In this paper, we consider higher-order interactions in the competitive processes of spatial rock-paper-scissors (RPS) dynamics, specifically within spatially embedded hyper-lattices, and investigate what biodiversity can be driven by HOIs. Considering hyperedges, species in hyperedges can be different, and different relationships are considered, which can eventually demonstrate the strength of competition. With the competition intensity modulated by the sensitivity of HOIs, extensive simulations have shown that higher-order competitive processes can promote coexistence. We also found that stratification of species densities occurs when three species coexist due to HOIs, which are closely related to the increase of empty sites and disordered spiral entanglement. From investigating the extinction probability in a broad aspect, it has been found that, even if HOIs are working, the coexistence in the system is eventually broken at high mobility regimes. The intensified sensitivity to HOIs can somewhat alleviate extinction, although no striking change has occurred. Our findings may address that modeling predator-prey interactions incorporating HOIs is important for gaining insights into biodiversity, and we hope our study may provide a broad aspect for exploring complex ecosystems.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129083"},"PeriodicalIF":3.5,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357283","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 : 2024-09-30DOI: 10.1016/j.amc.2024.129077
Leyi Zheng , Yimin Zhou
In this paper, a heterogeneous leader-follower multi-agent system is studied under simultaneous time-varying communication faults and actuator faults. First, the state of the leader is modeled as the closed-loop reference model (CRM) where the states of the direct-connected followers are fed to the leader to improve the leader-follower tracking capability. An event-triggered communication mechanism is designed for the agent information sharing among its neighbors so as to reduce the communication burden. The designed event-triggered mechanism, capable of adjusting the triggering interval threshold within a certain range, can be applied in practical multi-robot collaborative control to accommodate the varying requirements for different triggering intervals. Considering the time-varying communication link failures, a new distributed event-triggered observer is designed for each follower to estimate the system states so as to reduce the state error, whereas the adaptive distributed event-triggered estimators are further designed for the non-directly connected followers to estimate the coefficient matrix of the leader system. Then, an estimator is designed for the actuator fault estimation to mitigate their impact on the system consistency. Finally, an adaptive control strategy is proposed to ensure the consistency of the leader-follower system under the time-varying communication link faults and actuator faults. It is also shown that Zeno behavior is excluded for each agent and the effectiveness of the proposed adaptive event-triggered control strategy is verified on a heterogeneous multi-agent system.
{"title":"Event-triggered distributed consensus control of heterogeneous multi-agent system under communication and actuator faults","authors":"Leyi Zheng , Yimin Zhou","doi":"10.1016/j.amc.2024.129077","DOIUrl":"10.1016/j.amc.2024.129077","url":null,"abstract":"<div><div>In this paper, a heterogeneous leader-follower multi-agent system is studied under simultaneous time-varying communication faults and actuator faults. First, the state of the leader is modeled as the closed-loop reference model (CRM) where the states of the direct-connected followers are fed to the leader to improve the leader-follower tracking capability. An event-triggered communication mechanism is designed for the agent information sharing among its neighbors so as to reduce the communication burden. The designed event-triggered mechanism, capable of adjusting the triggering interval threshold within a certain range, can be applied in practical multi-robot collaborative control to accommodate the varying requirements for different triggering intervals. Considering the time-varying communication link failures, a new distributed event-triggered observer is designed for each follower to estimate the system states so as to reduce the state error, whereas the adaptive distributed event-triggered estimators are further designed for the non-directly connected followers to estimate the coefficient matrix of the leader system. Then, an estimator is designed for the actuator fault estimation to mitigate their impact on the system consistency. Finally, an adaptive control strategy is proposed to ensure the consistency of the leader-follower system under the time-varying communication link faults and actuator faults. It is also shown that Zeno behavior is excluded for each agent and the effectiveness of the proposed adaptive event-triggered control strategy is verified on a heterogeneous multi-agent system.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"487 ","pages":"Article 129077"},"PeriodicalIF":3.5,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357170","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}
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