Pub Date : 2024-09-28DOI: 10.1016/j.matcom.2024.09.026
Yong Yao
In this paper, the dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie–Gower predator–prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie–Gower predator–prey system such as two saddle–node bifurcations and one Bogdanov–Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Some numerical simulations are also provided to verify the theoretical results and evaluate their biological implications such as the changes of phase diagram near the degenerate equilibrium due to the Bogdanov–Takens bifurcation and the coexistence of multiple limit cycles arising from the degenerate Hopf bifurcation. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.
{"title":"Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey","authors":"Yong Yao","doi":"10.1016/j.matcom.2024.09.026","DOIUrl":"10.1016/j.matcom.2024.09.026","url":null,"abstract":"<div><div>In this paper, the dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie–Gower predator–prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie–Gower predator–prey system such as two saddle–node bifurcations and one Bogdanov–Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Some numerical simulations are also provided to verify the theoretical results and evaluate their biological implications such as the changes of phase diagram near the degenerate equilibrium due to the Bogdanov–Takens bifurcation and the coexistence of multiple limit cycles arising from the degenerate Hopf bifurcation. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 32-49"},"PeriodicalIF":4.4,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358544","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 : 2024-09-27DOI: 10.1016/j.matcom.2024.09.030
Supinder Kaur , Kalpana Dahiya , Anuj Sharma
Motivated by the hierarchical structure within transportation systems, this paper explores a two-phase time minimization transportation problem with restricted flow (). In this problem, the transportation of products occurs in two distinct phases due to the partition of source–destination links into two separate levels: Level-1 and Level-2 links, with a specified amount of commodity being transported in each phase. For the transportation of a specific quantity of goods during the first phase, only Level-1 links are utilized. Following this, during the second phase of transportation, only Level-2 links are utilized. Transportation is carried out concurrently via numerous source–destination links relevant to each phase. This paper proposes an iterative algorithm (Algorithm-) to find an optimal solution for a two-phase time minimization transportation problem that minimizes the sum of Phase-1 and Phase-2 transportation times. The proposed algorithm solves a solid time minimization transportation problemits restricted version at each iteration. Various theoretical results are proven to support the convergence of the algorithm. Numerical examples of various sizes are provided to support the theoretical results. Computational experiments conducted on randomly generated instances demonstrate the algorithm’s efficiency and convergence. The proposed algorithm offers an alternative method for solving two-phase time minimization transportation problems.
{"title":"Two-phase time minimization transportation problem with the restricted flow","authors":"Supinder Kaur , Kalpana Dahiya , Anuj Sharma","doi":"10.1016/j.matcom.2024.09.030","DOIUrl":"10.1016/j.matcom.2024.09.030","url":null,"abstract":"<div><div>Motivated by the hierarchical structure within transportation systems, this paper explores a two-phase time minimization transportation problem with restricted flow (<span><math><mrow><mn>2</mn><mi>p</mi><mo>−</mo><mi>T</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math></span>). In this problem, the transportation of products occurs in two distinct phases due to the partition of source–destination links into two separate levels: Level-1 and Level-2 links, with a specified amount of commodity being transported in each phase. For the transportation of a specific quantity of goods during the first phase, only Level-1 links are utilized. Following this, during the second phase of transportation, only Level-2 links are utilized. Transportation is carried out concurrently via numerous source–destination links relevant to each phase. This paper proposes an iterative algorithm (Algorithm-<span><math><mrow><mi>T</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math></span>) to find an optimal solution for a two-phase time minimization transportation problem that minimizes the sum of Phase-1 and Phase-2 transportation times. The proposed algorithm solves a solid time minimization transportation problem<span><math><mo>∖</mo></math></span>its restricted version at each iteration. Various theoretical results are proven to support the convergence of the algorithm. Numerical examples of various sizes are provided to support the theoretical results. Computational experiments conducted on randomly generated instances demonstrate the algorithm’s efficiency and convergence. The proposed algorithm offers an alternative method for solving two-phase time minimization transportation problems.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 611-635"},"PeriodicalIF":4.4,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530191","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 : 2024-09-26DOI: 10.1016/j.matcom.2024.09.018
Yichen Su, Leevan Ling
Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels with high orders of smoothness on some sufficiently dense set of trial centers provides high spatial approximation accuracy that can exceed the accuracy of finite difference methods in time. The paper proposes a greedy approach for selecting trial subspaces in the kernel-based collocation method applied to time-stepping to balance errors in both well-conditioned and ill-conditioned scenarios. The approach involves selecting trial centers using a fast block-greedy algorithm with new stopping criteria that aim to balance temporal and spatial errors. Numerical simulations of coupled bulk-surface pattern formations, a system involving two functions in the domain and two on the boundary, illustrate the effectiveness of the proposed method in reducing trial space dimensions while maintaining accuracy.
{"title":"Greedy trial subspace selection in meshfree time-stepping scheme with applications in coupled bulk-surface pattern formations","authors":"Yichen Su, Leevan Ling","doi":"10.1016/j.matcom.2024.09.018","DOIUrl":"10.1016/j.matcom.2024.09.018","url":null,"abstract":"<div><div>Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels with high orders of smoothness on some sufficiently dense set of trial centers provides high spatial approximation accuracy that can exceed the accuracy of finite difference methods in time. The paper proposes a greedy approach for selecting trial subspaces in the kernel-based collocation method applied to time-stepping to balance errors in both well-conditioned and ill-conditioned scenarios. The approach involves selecting trial centers using a fast block-greedy algorithm with new stopping criteria that aim to balance temporal and spatial errors. Numerical simulations of coupled bulk-surface pattern formations, a system involving two functions in the domain and two on the boundary, illustrate the effectiveness of the proposed method in reducing trial space dimensions while maintaining accuracy.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 498-513"},"PeriodicalIF":4.4,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328105","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 : 2024-09-26DOI: 10.1016/j.matcom.2024.09.023
K. Janani , S.S. Mohanrasu , Ardak Kashkynbayev , R. Rakkiyappan
Feature selection is a crucial step in the process of preparing and refining data. By identifying and retaining only the most informative and discriminative features, one can achieve several benefits, including faster training times, reduced risk of overfitting, improved model generalization, and enhanced interpretability. Ensemble feature selection has demonstrated its efficacy in improving the stability and generalization performance of models and is particularly valuable in high-dimensional datasets and complex machine learning tasks, contributing to the creation of more accurate and robust predictive models. This article presents an innovative ensemble feature selection technique through the development of a unique Multi-criteria decision making (MCDM) model, incorporating both rank aggregation principles and a filter-based algorithm. The proposed MCDM model combines the Combined Compromise Solution (CoCoSo) method and the Archimedean operator within interval-valued intuitionistic fuzzy environments, effectively addressing the challenges of vagueness and imprecision in datasets. A customizable feature selection model is introduced, allowing users to define the number of features, employing a sigmoidal function with a tuning parameter for fuzzification. The assignment of entropy weights in the Interval-valued intuitionistic fuzzy set (IVIFS) environment provides priorities to each column. The method’s effectiveness is assessed on real-world datasets, comparing it with existing approaches and validated through statistical tests such as the Friedman test and post-hoc Conover test, emphasizing its significance in comparison to current methodologies. Based on the results obtained, we inferred that our structured approach to ensemble feature selection, utilizing a specific case of the Archimedean operator, demonstrated superior performance across the datasets. This more generalized methodology enhances the robustness and effectiveness of feature selection by leveraging the strengths of the Archimedean operator, resulting in improved data analysis and model accuracy.
{"title":"Ensemble feature selection via CoCoSo method extended to interval-valued intuitionistic fuzzy environment","authors":"K. Janani , S.S. Mohanrasu , Ardak Kashkynbayev , R. Rakkiyappan","doi":"10.1016/j.matcom.2024.09.023","DOIUrl":"10.1016/j.matcom.2024.09.023","url":null,"abstract":"<div><div>Feature selection is a crucial step in the process of preparing and refining data. By identifying and retaining only the most informative and discriminative features, one can achieve several benefits, including faster training times, reduced risk of overfitting, improved model generalization, and enhanced interpretability. Ensemble feature selection has demonstrated its efficacy in improving the stability and generalization performance of models and is particularly valuable in high-dimensional datasets and complex machine learning tasks, contributing to the creation of more accurate and robust predictive models. This article presents an innovative ensemble feature selection technique through the development of a unique Multi-criteria decision making (MCDM) model, incorporating both rank aggregation principles and a filter-based algorithm. The proposed MCDM model combines the Combined Compromise Solution (CoCoSo) method and the Archimedean operator within interval-valued intuitionistic fuzzy environments, effectively addressing the challenges of vagueness and imprecision in datasets. A customizable feature selection model is introduced, allowing users to define the number of features, employing a sigmoidal function with a tuning parameter for fuzzification. The assignment of entropy weights in the Interval-valued intuitionistic fuzzy set (IVIFS) environment provides priorities to each column. The method’s effectiveness is assessed on real-world datasets, comparing it with existing approaches and validated through statistical tests such as the Friedman test and post-hoc Conover test, emphasizing its significance in comparison to current methodologies. Based on the results obtained, we inferred that our structured approach to ensemble feature selection, utilizing a specific case of the Archimedean operator, demonstrated superior performance across the datasets. This more generalized methodology enhances the robustness and effectiveness of feature selection by leveraging the strengths of the Archimedean operator, resulting in improved data analysis and model accuracy.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 50-77"},"PeriodicalIF":4.4,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358545","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 : 2024-09-26DOI: 10.1016/j.matcom.2024.09.020
Peng Wu
In this paper, we study the global well-posedness and global dynamics of a reaction–diffusion HIV infection model with the chemotactic movement of CTLs (Cytotoxic T lymphocytes). We first show the global existence and uniform boundedness for solutions of the system with general functional incidences. Then, for the model with bilinear incidence rate, we discuss the existence conditions of the three equilibria (infection-free, chemokines-extinct, chemokines-acute equilibria) of the model and obtain the conclusion of the local asymptotic stability of these equilibria by analyzing the linearized system at these equilibria. Moreover, by constructing reasonable Lyapunov functionals, we investigate the global stability and attractivity of the equilibria. Applying the estimate, Young’s inequality, Gagiardo-Nirenberg inequality and the parabolic regularity theorem, we also discuss the convergence rates of the equilibria. Finally, some numerical simulations are conducted to verify the theoretical results.
在本文中，我们研究了带有 CTL（细胞毒性 T 淋巴细胞）趋化运动的反应扩散型 HIV 感染模型的全局拟合性和全局动力学。我们首先证明了具有一般函数发生率的系统解的全局存在性和均匀有界性。然后，对于具有双线性发病率的模型，我们讨论了模型的三个平衡点（无感染平衡点、趋化因子-灭绝平衡点、趋化因子-急性平衡点）的存在条件，并通过分析这些平衡点处的线性化系统，得出了这些平衡点的局部渐近稳定性结论。此外，通过构建合理的 Lyapunov 函数，我们还研究了均衡点的全局稳定性和吸引力。应用 Lp-Lq 估计、Young 不等式、Gagiardo-Nirenberg 不等式和抛物线正则定理，我们还讨论了均衡点的收敛率。最后，我们进行了一些数值模拟来验证理论结果。
{"title":"Global well-posedness and dynamics of spatial diffusion HIV model with CTLs response and chemotaxis","authors":"Peng Wu","doi":"10.1016/j.matcom.2024.09.020","DOIUrl":"10.1016/j.matcom.2024.09.020","url":null,"abstract":"<div><div>In this paper, we study the global well-posedness and global dynamics of a reaction–diffusion HIV infection model with the chemotactic movement of CTLs (Cytotoxic T lymphocytes). We first show the global existence and uniform boundedness for solutions of the system with general functional incidences. Then, for the model with bilinear incidence rate, we discuss the existence conditions of the three equilibria (infection-free, chemokines-extinct, chemokines-acute equilibria) of the model and obtain the conclusion of the local asymptotic stability of these equilibria by analyzing the linearized system at these equilibria. Moreover, by constructing reasonable Lyapunov functionals, we investigate the global stability and attractivity of the equilibria. Applying the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>−</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></mrow></math></span> estimate, Young’s inequality, Gagiardo-Nirenberg inequality and the parabolic regularity theorem, we also discuss the convergence rates of the equilibria. Finally, some numerical simulations are conducted to verify the theoretical results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 402-417"},"PeriodicalIF":4.4,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328274","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 : 2024-09-25DOI: 10.1016/j.matcom.2024.09.016
Bohumír Bastl, Kristýna Slabá
In this paper, we deal with adaptive refinement in numerical simulation of incompressible flow solved by isogeometric analysis. We study various error estimators and compare them with respect to convergence to the exact solution. Further, we propose a new class of error estimators based on stabilization methods for numerical solving of incompressible flow and we show that they provide viable option to standard error estimators. Moreover, we comment on different choices of marking strategies and their suitability to the case of incompressible flow and provide comparison of error estimators also with respect to selected marking strategies and selected representative pairs of discretization spaces in isogeometric analysis.
{"title":"Adaptive refinement in incompressible fluid flow simulation based on THB-splines-powered isogeometric analysis","authors":"Bohumír Bastl, Kristýna Slabá","doi":"10.1016/j.matcom.2024.09.016","DOIUrl":"10.1016/j.matcom.2024.09.016","url":null,"abstract":"<div><div>In this paper, we deal with adaptive refinement in numerical simulation of incompressible flow solved by isogeometric analysis. We study various error estimators and compare them with respect to convergence to the exact solution. Further, we propose a new class of error estimators based on stabilization methods for numerical solving of incompressible flow and we show that they provide viable option to standard error estimators. Moreover, we comment on different choices of marking strategies and their suitability to the case of incompressible flow and provide comparison of error estimators also with respect to selected marking strategies and selected representative pairs of discretization spaces in isogeometric analysis.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 514-533"},"PeriodicalIF":4.4,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357113","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 : 2024-09-24DOI: 10.1016/j.matcom.2024.09.019
Longyuan Wu , Xufeng Xiao , Shuying Zhai
The evolution of a dynamic system on complex curved 3D surfaces is essential for the understanding of natural phenomena, the development of new materials, and engineering design optimization. In this work, we study the viscous Cahn–Hilliard equation on curved surfaces and develop two linear energy stable finite element schemes based on the lumped mass method. Two stabilizing terms are added to ensure both the unique solvability and unconditional energy stability. We prove rigorously that two schemes are unconditionally energy stable . Numerical experiments are presented to verify theoretical results and to show the robustness and accuracy of the proposed method.
{"title":"Two linear energy stable lumped mass finite element schemes for the viscous Cahn–Hilliard equation on curved surfaces in 3D","authors":"Longyuan Wu , Xufeng Xiao , Shuying Zhai","doi":"10.1016/j.matcom.2024.09.019","DOIUrl":"10.1016/j.matcom.2024.09.019","url":null,"abstract":"<div><div>The evolution of a dynamic system on complex curved 3D surfaces is essential for the understanding of natural phenomena, the development of new materials, and engineering design optimization. In this work, we study the viscous Cahn–Hilliard equation on curved surfaces and develop two linear energy stable finite element schemes based on the lumped mass method. Two stabilizing terms are added to ensure both the unique solvability and unconditional energy stability. We prove rigorously that two schemes are unconditionally energy stable . Numerical experiments are presented to verify theoretical results and to show the robustness and accuracy of the proposed method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 418-430"},"PeriodicalIF":4.4,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328275","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 : 2024-09-24DOI: 10.1016/j.matcom.2024.09.022
Xubin Jiao , Li Liu , Xiao Yu
To reflect the harvesting effect, a nonsmooth Filippov Leslie–Gower predator–prey model is proposed. Unlike traditional Filippov models, the time delay and reaction–diffusion under the condition of homogeneous Neumann boundary are considered in our system. The stability of equilibrium and the existence of the spatial Hopf bifurcation of the subsystems at the positive equilibrium are investigated. Furthermore, a comprehensive analysis is conducted on the sliding mode dynamics as well as the regular, virtual, and pseudoequilibria. The findings reveal that our Filippov system exhibits either a globally asymptotically stable regular equilibrium, a globally asymptotically stable time periodic solution, or a globally asymptotically stable pseudoequilibrium, contingent upon the specific values of the time delay and threshold level. A boundary point bifurcation, which transform a stable equilibrium point or periodic solution into a stable pseudoequilibrium, is demonstrated to emphasize the impact of time delay on our Filippov system and the significance of threshold control. Meanwhile, two kinds of global sliding bifurcations are exhibited, which sequentially transform a stable periodic solutions below the threshold into a grazing, sliding switching, and crossing bifurcations, depending on changes in the time delay or threshold level. Our results indicate that bucking bifurcation and crossing bifurcation pose significant challenges to the control of our Filippov system.
{"title":"Rich dynamics of a reaction–diffusion Filippov Leslie–Gower predator–prey model with time delay and discontinuous harvesting","authors":"Xubin Jiao , Li Liu , Xiao Yu","doi":"10.1016/j.matcom.2024.09.022","DOIUrl":"10.1016/j.matcom.2024.09.022","url":null,"abstract":"<div><div>To reflect the harvesting effect, a nonsmooth Filippov Leslie–Gower predator–prey model is proposed. Unlike traditional Filippov models, the time delay and reaction–diffusion under the condition of homogeneous Neumann boundary are considered in our system. The stability of equilibrium and the existence of the spatial Hopf bifurcation of the subsystems at the positive equilibrium are investigated. Furthermore, a comprehensive analysis is conducted on the sliding mode dynamics as well as the regular, virtual, and pseudoequilibria. The findings reveal that our Filippov system exhibits either a globally asymptotically stable regular equilibrium, a globally asymptotically stable time periodic solution, or a globally asymptotically stable pseudoequilibrium, contingent upon the specific values of the time delay and threshold level. A boundary point bifurcation, which transform a stable equilibrium point or periodic solution into a stable pseudoequilibrium, is demonstrated to emphasize the impact of time delay on our Filippov system and the significance of threshold control. Meanwhile, two kinds of global sliding bifurcations are exhibited, which sequentially transform a stable periodic solutions below the threshold into a grazing, sliding switching, and crossing bifurcations, depending on changes in the time delay or threshold level. Our results indicate that bucking bifurcation and crossing bifurcation pose significant challenges to the control of our Filippov system.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 339-361"},"PeriodicalIF":4.4,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323339","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}
Seeking shelter from threats is a widespread instinct across species, specially employed by prey to avoid direct confrontations with predators. The present investigation centers on a three-species food chain model wherein the basal prey, characterized by logistic growth, seeks refuge to evade the intermediate predator, while the intermediate predator, in turn, seeks refuge to avoid encounters with the top predator. Additionally, our model assumes that the presence of the top predator induces a mate-finding Allee effect among the intermediate predator. We investigate how varying levels of refuge, along with other critical parameters such as the reproduction rate of the basal prey and the natural mortality rate of the top predator, influence system’s dynamics within the biparametric planes. Our model displays multistability and undergoes transcritical, saddle–node, Bogdanov–Takens and cusp bifurcations across different parameters. Moreover, the external environmental noise can induce interesting dynamics in the predator–prey system, resulting in noise-induced frequent transitions between distinct interior attractors or from interior to axial attractors. This phenomenon is particularly notable in scenarios where the deterministic model exhibits tristability. In summary, our findings offer potential new avenues for developing control strategies within the realm of community ecology in constant as well as fluctuating environments.
{"title":"Bifurcation analysis and exploration of noise-induced transitions of a food chain model with Allee effect","authors":"Sayan Mandal , Sudip Samanta , Pankaj Kumar Tiwari , Ranjit Kumar Upadhyay","doi":"10.1016/j.matcom.2024.09.015","DOIUrl":"10.1016/j.matcom.2024.09.015","url":null,"abstract":"<div><div>Seeking shelter from threats is a widespread instinct across species, specially employed by prey to avoid direct confrontations with predators. The present investigation centers on a three-species food chain model wherein the basal prey, characterized by logistic growth, seeks refuge to evade the intermediate predator, while the intermediate predator, in turn, seeks refuge to avoid encounters with the top predator. Additionally, our model assumes that the presence of the top predator induces a mate-finding Allee effect among the intermediate predator. We investigate how varying levels of refuge, along with other critical parameters such as the reproduction rate of the basal prey and the natural mortality rate of the top predator, influence system’s dynamics within the biparametric planes. Our model displays multistability and undergoes transcritical, saddle–node, Bogdanov–Takens and cusp bifurcations across different parameters. Moreover, the external environmental noise can induce interesting dynamics in the predator–prey system, resulting in noise-induced frequent transitions between distinct interior attractors or from interior to axial attractors. This phenomenon is particularly notable in scenarios where the deterministic model exhibits tristability. In summary, our findings offer potential new avenues for developing control strategies within the realm of community ecology in constant as well as fluctuating environments.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 313-338"},"PeriodicalIF":4.4,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323338","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}
Grid-forming control techniques are required to achieve a high penetration of power electronics-based renewable energy sources for decarbonized electric systems. However, different grid-forming control strategies can operate in the same grid, and grid stability shall be warranted. This paper analyses the use of different grid-forming control strategies for diode rectifier-based wind power plants. The analysed grid-forming controllers are the well-known droop control, an advanced droop control, and the virtual synchronous machine control. The controllers’ analysis validates the three grid-forming controllers’ interoperability, identifying each control parameter’s contribution to the stability of each system state variable. Furthermore, the analysis allows a better tuning of the control parameters. Additionally, a fault-ride-through strategy that improves the system restoration after faults is proposed and validated. The proposed fault-ride-through strategy achieves a soft restoration of the active power.
{"title":"Analysis of non-uniform grid-forming control techniques for the HVDC connection of renewable energy","authors":"Adrián Beneit-Barajas, Patricia Penades-Huesca, Jaime Martínez-Turégano","doi":"10.1016/j.matcom.2024.09.014","DOIUrl":"10.1016/j.matcom.2024.09.014","url":null,"abstract":"<div><div>Grid-forming control techniques are required to achieve a high penetration of power electronics-based renewable energy sources for decarbonized electric systems. However, different grid-forming control strategies can operate in the same grid, and grid stability shall be warranted. This paper analyses the use of different grid-forming control strategies for diode rectifier-based wind power plants. The analysed grid-forming controllers are the well-known droop control, an advanced droop control, and the virtual synchronous machine control. The controllers’ analysis validates the three grid-forming controllers’ interoperability, identifying each control parameter’s contribution to the stability of each system state variable. Furthermore, the analysis allows a better tuning of the control parameters. Additionally, a fault-ride-through strategy that improves the system restoration after faults is proposed and validated. The proposed fault-ride-through strategy achieves a soft restoration of the active power.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"229 ","pages":"Pages 1-14"},"PeriodicalIF":4.4,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142358546","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}
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