Pub Date : 2025-01-12DOI: 10.1016/j.matcom.2025.01.002
Hanghang Wu , Hongqi Yang
This paper studies a time-fractional diffusion ill-posed inverse source problem. We use a simplified Tikhonov regularization method and a Fourier regularization method to solve the problem. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori error estimates are derived. Among them, the a priori error estimate derived from the simplified Tikhonov regularization method is optimal, while the a posteriori error estimate is quasi-optimal. The a priori and a posteriori error estimates derived by the Fourier regularization method are both optimal. Finally, numerical examples are conducted to demonstrate the effectiveness and stability of the proposed regularization methods.
{"title":"Regularization methods for solving a time-fractional diffusion inverse source problem","authors":"Hanghang Wu , Hongqi Yang","doi":"10.1016/j.matcom.2025.01.002","DOIUrl":"10.1016/j.matcom.2025.01.002","url":null,"abstract":"<div><div>This paper studies a time-fractional diffusion ill-posed inverse source problem. We use a simplified Tikhonov regularization method and a Fourier regularization method to solve the problem. Under the selection rules of a priori and a posteriori regularization parameters, a priori and a posteriori error estimates are derived. Among them, the a priori error estimate derived from the simplified Tikhonov regularization method is optimal, while the a posteriori error estimate is quasi-optimal. The a priori and a posteriori error estimates derived by the Fourier regularization method are both optimal. Finally, numerical examples are conducted to demonstrate the effectiveness and stability of the proposed regularization methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 295-310"},"PeriodicalIF":4.4,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268910","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 : 2025-01-11DOI: 10.1016/j.matcom.2025.01.008
Peng-Fei Han , Ru-Suo Ye , Yi Zhang
The challenge of solving the initial value problem for the coupled Lakshmanan–Porsezian–Daniel equations which involves non-zero boundary conditions at infinity is addressed by the development of a suitable inverse scattering transform. Analytical properties of the Jost eigenfunctions are examined, along with the analysis of scattering coefficient characteristics. This analysis not only leads to the derivation of additional auxiliary eigenfunctions but also is necessary for a comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed for studying the eigenfunctions and scattering coefficients. These symmetry results are utilized to rigorously define the discrete spectrum and ascertain the corresponding symmetries of scattering datas. The inverse scattering problem is formulated by the Riemann–Hilbert problem. Subsequently, we derive analytical solutions from the coupled Lakshmanan–Porsezian–Daniel equations with a detailed examination of the novel soliton solutions.
{"title":"Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications","authors":"Peng-Fei Han , Ru-Suo Ye , Yi Zhang","doi":"10.1016/j.matcom.2025.01.008","DOIUrl":"10.1016/j.matcom.2025.01.008","url":null,"abstract":"<div><div>The challenge of solving the initial value problem for the coupled Lakshmanan–Porsezian–Daniel equations which involves non-zero boundary conditions at infinity is addressed by the development of a suitable inverse scattering transform. Analytical properties of the Jost eigenfunctions are examined, along with the analysis of scattering coefficient characteristics. This analysis not only leads to the derivation of additional auxiliary eigenfunctions but also is necessary for a comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed for studying the eigenfunctions and scattering coefficients. These symmetry results are utilized to rigorously define the discrete spectrum and ascertain the corresponding symmetries of scattering datas. The inverse scattering problem is formulated by the Riemann–Hilbert problem. Subsequently, we derive analytical solutions from the coupled Lakshmanan–Porsezian–Daniel equations with a detailed examination of the novel soliton solutions.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 483-503"},"PeriodicalIF":4.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367923","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 : 2025-01-11DOI: 10.1016/j.matcom.2024.12.020
Alessandro Alla , Marco Berardi , Luca Saluzzi
We present an approach for the optimization of irrigation in a Richards’ equation framework. We introduce a proper cost functional, aimed at minimizing the amount of water provided by irrigation, at the same time maximizing the root water uptake, which is modeled by a sink term in the continuity equation. The control is acting on the boundary of the dynamics and due to the nature of the mathematical problem we use a State Dependent Riccati approach which provides suboptimal control in feedback form, applied to the system of ODEs resulting from the Richards’ equation semidiscretization in space. The problem is tested with existing hydraulic parameters, also considering proper root water uptake functions. The numerical simulations also consider the presence of noise in the model to further validate the use of a feedback control approach.
{"title":"State Dependent Riccati for dynamic boundary control to optimize irrigation in Richards’ equation framework","authors":"Alessandro Alla , Marco Berardi , Luca Saluzzi","doi":"10.1016/j.matcom.2024.12.020","DOIUrl":"10.1016/j.matcom.2024.12.020","url":null,"abstract":"<div><div>We present an approach for the optimization of irrigation in a Richards’ equation framework. We introduce a proper cost functional, aimed at minimizing the amount of water provided by irrigation, at the same time maximizing the root water uptake, which is modeled by a sink term in the continuity equation. The control is acting on the boundary of the dynamics and due to the nature of the mathematical problem we use a State Dependent Riccati approach which provides suboptimal control in feedback form, applied to the system of ODEs resulting from the Richards’ equation semidiscretization in space. The problem is tested with existing hydraulic parameters, also considering proper root water uptake functions. The numerical simulations also consider the presence of noise in the model to further validate the use of a feedback control approach.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 261-275"},"PeriodicalIF":4.4,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367924","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 : 2025-01-10DOI: 10.1016/j.matcom.2025.01.001
Pushpendra Kumar , Tae H. Lee , Vedat Suat Erturk
In this paper, we propose a novel fractional-order neutral-type delay neural network (FNDNN) considering two delay variables in terms of the Caputo fractional derivatives. We prove the existence of a unique solution within the given time domain. We analyse the bifurcation with respect to both delay parameters and the initial state’s stability of the FNDNN. We derive the numerical solution of the proposed FNDNN using a recently proposed algorithm. We provide the necessary graphical simulations to justify the correctness of our theoretical proofs. We investigate how both delay parameters affect stability and induce bifurcations in the FNDNN. Also, we check the influence of fractional orders on the dynamical behaviour of the FNDNN. We find that, in comparison with the integer-order case, the proposed FNDNN has faster convergence performance.
{"title":"A novel fractional-order neutral-type two-delayed neural network: Stability, bifurcation, and numerical solution","authors":"Pushpendra Kumar , Tae H. Lee , Vedat Suat Erturk","doi":"10.1016/j.matcom.2025.01.001","DOIUrl":"10.1016/j.matcom.2025.01.001","url":null,"abstract":"<div><div>In this paper, we propose a novel fractional-order neutral-type delay neural network (FNDNN) considering two delay variables in terms of the Caputo fractional derivatives. We prove the existence of a unique solution within the given time domain. We analyse the bifurcation with respect to both delay parameters and the initial state’s stability of the FNDNN. We derive the numerical solution of the proposed FNDNN using a recently proposed algorithm. We provide the necessary graphical simulations to justify the correctness of our theoretical proofs. We investigate how both delay parameters affect stability and induce bifurcations in the FNDNN. Also, we check the influence of fractional orders on the dynamical behaviour of the FNDNN. We find that, in comparison with the integer-order case, the proposed FNDNN has faster convergence performance.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 245-260"},"PeriodicalIF":4.4,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367928","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 : 2025-01-08DOI: 10.1016/j.matcom.2024.12.022
M.F. Carfora , F. Iovanna , I. Torcicollo
Intraguild predation, representing a true combination of predation and competition between two species that rely on a common resource, is of foremost importance in many natural communities. We investigate a spatial model of three species interaction, characterized by a Holling type II functional response and linear cross-diffusion. For this model we report necessary and sufficient conditions ensuring the insurgence of Turing instability for the coexistence equilibrium; we also obtain conditions characterizing the different patterns by multiple scale analysis. Numerical experiments confirm the occurrence of different scenarios of Turing instability, also including Turing–Hopf patterns.
{"title":"Turing patterns in an intraguild predator–prey model","authors":"M.F. Carfora , F. Iovanna , I. Torcicollo","doi":"10.1016/j.matcom.2024.12.022","DOIUrl":"10.1016/j.matcom.2024.12.022","url":null,"abstract":"<div><div>Intraguild predation, representing a true combination of predation and competition between two species that rely on a common resource, is of foremost importance in many natural communities. We investigate a spatial model of three species interaction, characterized by a Holling type II functional response and linear cross-diffusion. For this model we report necessary and sufficient conditions ensuring the insurgence of Turing instability for the coexistence equilibrium; we also obtain conditions characterizing the different patterns by multiple scale analysis. Numerical experiments confirm the occurrence of different scenarios of Turing instability, also including Turing–Hopf patterns.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 192-210"},"PeriodicalIF":4.4,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269207","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 : 2025-01-08DOI: 10.1016/j.matcom.2025.01.005
Hesong Li , Zhaoting Li , Hongbo Zhang , Yi Wang
This paper presents an adaptive mesh refinement method that considers control errors for solving pseudospectral optimal control problems. Firstly, a method for estimating errors in both states and controls is presented. Based on the estimation results, an adaptive mesh refinement method is subsequently devised. This method increases and reduces the number of collocation points in accordance with a theoretical convergence rate that incorporates both state and control errors. Furthermore, in addition to dividing intervals resulting from a large number of collocation points, new intervals are also generated when control errors exceed tolerance. As a result, the mesh density near the point with the largest control error is effectively increased, thereby improving the discretization accuracy. The effectiveness of the method is illustrated through three numerical examples, and its performance is evaluated in comparison to other adaptive mesh refinement methods. The numerical results demonstrate that the proposed method exhibits superior performance in terms of capturing the nonsmooth and discontinuous changes and achieving an accurate solution, while requiring fewer iterations.
{"title":"An adaptive mesh refinement method considering control errors for pseudospectral discretization","authors":"Hesong Li , Zhaoting Li , Hongbo Zhang , Yi Wang","doi":"10.1016/j.matcom.2025.01.005","DOIUrl":"10.1016/j.matcom.2025.01.005","url":null,"abstract":"<div><div>This paper presents an adaptive mesh refinement method that considers control errors for solving pseudospectral optimal control problems. Firstly, a method for estimating errors in both states and controls is presented. Based on the estimation results, an adaptive mesh refinement method is subsequently devised. This method increases and reduces the number of collocation points in accordance with a theoretical convergence rate that incorporates both state and control errors. Furthermore, in addition to dividing intervals resulting from a large number of collocation points, new intervals are also generated when control errors exceed tolerance. As a result, the mesh density near the point with the largest control error is effectively increased, thereby improving the discretization accuracy. The effectiveness of the method is illustrated through three numerical examples, and its performance is evaluated in comparison to other adaptive mesh refinement methods. The numerical results demonstrate that the proposed method exhibits superior performance in terms of capturing the nonsmooth and discontinuous changes and achieving an accurate solution, while requiring fewer iterations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 140-159"},"PeriodicalIF":4.4,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268913","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 : 2025-01-04DOI: 10.1016/j.matcom.2024.12.027
Youssra Hajri, Saida Amine
This paper presents a delayed within-host model to investigate the intricate dynamics of HIV/SARS-CoV-2 co-infection. The analysis establishes the existence of unique positive and bounded solutions under specified initial conditions. The healthy, the single HIV infection, the single SARS-CoV-2 infection and the HIV/SARS-CoV-2 co-infection steady states, are computed contingent upon threshold parameters , , and . Through rigorous examination of characteristic equations, the local stability of pivotal steady states-namely, the healthy state and the HIV/SARS-CoV-2 co-infection state is elucidated, alongside the identification of Hopf bifurcations using delays as bifurcation parameters. Intriguingly, theoretical analyses reveal that delays exert no discernible influence on the stability of the healthy state, whereas they may destabilize the HIV/SARS-CoV-2 co-infection state under specific conditions. Moreover, employing appropriate Lyapunov functions confirms the global asymptotic stability of all steady states. Complementary numerical simulations are conducted to augment theoretical insights and delineate the nuanced impact of each time delay, albeit without explicit Hopf bifurcation simulations.
{"title":"Dynamics of a within-host HIV/SARS-CoV-2 co-infection model with two intracellular delays","authors":"Youssra Hajri, Saida Amine","doi":"10.1016/j.matcom.2024.12.027","DOIUrl":"10.1016/j.matcom.2024.12.027","url":null,"abstract":"<div><div>This paper presents a delayed within-host model to investigate the intricate dynamics of HIV/SARS-CoV-2 co-infection. The analysis establishes the existence of unique positive and bounded solutions under specified initial conditions. The healthy, the single HIV infection, the single SARS-CoV-2 infection and the HIV/SARS-CoV-2 co-infection steady states, are computed contingent upon threshold parameters <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>C</mi></mrow></msub></math></span>, and <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>H</mi><mi>C</mi></mrow></msub></math></span>. Through rigorous examination of characteristic equations, the local stability of pivotal steady states-namely, the healthy state and the HIV/SARS-CoV-2 co-infection state is elucidated, alongside the identification of Hopf bifurcations using delays as bifurcation parameters. Intriguingly, theoretical analyses reveal that delays exert no discernible influence on the stability of the healthy state, whereas they may destabilize the HIV/SARS-CoV-2 co-infection state under specific conditions. Moreover, employing appropriate Lyapunov functions confirms the global asymptotic stability of all steady states. Complementary numerical simulations are conducted to augment theoretical insights and delineate the nuanced impact of each time delay, albeit without explicit Hopf bifurcation simulations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 160-191"},"PeriodicalIF":4.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268914","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}
The paper presents a numerical solution of a higher-order nonlocal and nonlinear boundary value problem (NNBVP); it exhibits triple nonlinearities: nonlinear ordinary differential equation (ODE), nonlinear local boundary values and nonlinear integral boundary conditions (BCs). We consider one nonlocal, two nonlocal and three nonlocal BCs. New variables are incorporated, whose values at right-end present the integral parts in the specified nonlocal BCs. For an extremely precise solution of NNBVP, it is crucial to acquire highly accurate initial values of independent variables by solving target equations very accurately. Because of the implicit form of the target equations, they are solved by a fixed quasi-Newton method (FQNM) without calculating the differentials, which together with the shooting technique would offer nearly exact initial values. Higher-order numerical examples are examined to assure that the proposed methods are efficient to achieve some highly accurate solutions with 14- and 15-digit precisions, whose computational costs are very saving as reflected in the small number of iterations. The computed order of convergence (COC) reveals that the iterative methods converge faster than linear convergence. The novelty lies on the introduction of new variables to present the nonlocal boundary conditions, and develop FQNM to solve the target equations. The difficult part of nonlinear and nonlocal BC is simply transformed to find an ended value of the new variable governed by an ODE. When the constant iteration matrix is properly established, the numerical examples of NNBVP reveal that FQNM is convergent fast and is not sensitive to the initial guesses of unknown initial values.
{"title":"Solving higher-order nonlocal boundary value problems with high precision by the fixed quasi Newton methods","authors":"Chein-Shan Liu , Yung-Wei Chen , Jian-Hung Shen , Yen-Shen Chang","doi":"10.1016/j.matcom.2024.12.024","DOIUrl":"10.1016/j.matcom.2024.12.024","url":null,"abstract":"<div><div>The paper presents a numerical solution of a higher-order nonlocal and nonlinear boundary value problem (NNBVP); it exhibits triple nonlinearities: nonlinear ordinary differential equation (ODE), nonlinear local boundary values and nonlinear integral boundary conditions (BCs). We consider one nonlocal, two nonlocal and three nonlocal BCs. New variables are incorporated, whose values at right-end present the integral parts in the specified nonlocal BCs. For an extremely precise solution of NNBVP, it is crucial to acquire highly accurate initial values of independent variables by solving target equations very accurately. Because of the implicit form of the target equations, they are solved by a fixed quasi-Newton method (FQNM) without calculating the differentials, which together with the shooting technique would offer nearly exact initial values. Higher-order numerical examples are examined to assure that the proposed methods are efficient to achieve some highly accurate solutions with 14- and 15-digit precisions, whose computational costs are very saving as reflected in the small number of iterations. The computed order of convergence (<em>COC</em>) reveals that the iterative methods converge faster than linear convergence. The novelty lies on the introduction of new variables to present the nonlocal boundary conditions, and develop FQNM to solve the target equations. The difficult part of nonlinear and nonlocal BC is simply transformed to find an ended value of the new variable governed by an ODE. When the constant iteration matrix is properly established, the numerical examples of NNBVP reveal that FQNM is convergent fast and is not sensitive to the initial guesses of unknown initial values.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 211-226"},"PeriodicalIF":4.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143268912","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 : 2025-01-04DOI: 10.1016/j.matcom.2024.12.026
Sengen Hu, Liangqiang Zhou
This paper studies the lateral oscillations of pedestrian walking on a vibrating ground with a known motion, which can be modeled by a hybrid Rayleigh–van der Pol–Duffing oscillator with quintic nonlinearity and dual parametric excitations. The focus of the work is on the global dynamics of the oscillator, including chaos and subharmonic bifurcations. It reveals that the system can be subdivided into three categories in the undisturbed case: single well, double hump, and triple well. Specifically, the exact solutions for homoclinic, heteroclinic and subharmonic orbits in triple-well case are obtained analytically. The Melnikov method is employed to investigate the chaotic phenomena resulting from different orbits. Compared to a single self-excited oscillator, this hybrid oscillator exhibits higher sensitivity to external excitation and strong nonlinear terms. By adjusting the system parameters, the peak value of the chaos threshold can be controlled to avoid the occurrence of chaos. Based on the subharmonic Melnikov method, the subharmonic bifurcations of the system are examined and the extreme case is discussed. Some nonlinear phenomena are discovered. The system only exhibits chaotic behavior when there is a strong resonance, that is, when there is an integer-order subharmonic bifurcation. Furthermore, we find the pathways to chaos though subharmonic bifurcations encompass two distinct mechanisms: odd and even finite bifurcation sequences. The numerical simulation serves to verify the findings of the preceding analysis, while simultaneously elucidating a number of additional dynamic phenomena, including multi-stable state motion, bursting oscillations, and the coexistence of attractors.
{"title":"Global dynamics in the lateral oscillation model of pedestrian walking on a vibrating surface","authors":"Sengen Hu, Liangqiang Zhou","doi":"10.1016/j.matcom.2024.12.026","DOIUrl":"10.1016/j.matcom.2024.12.026","url":null,"abstract":"<div><div>This paper studies the lateral oscillations of pedestrian walking on a vibrating ground with a known motion, which can be modeled by a hybrid Rayleigh–van der Pol–Duffing oscillator with quintic nonlinearity and dual parametric excitations. The focus of the work is on the global dynamics of the oscillator, including chaos and subharmonic bifurcations. It reveals that the system can be subdivided into three categories in the undisturbed case: single well, double hump, and triple well. Specifically, the exact solutions for homoclinic, heteroclinic and subharmonic orbits in triple-well case are obtained analytically. The Melnikov method is employed to investigate the chaotic phenomena resulting from different orbits. Compared to a single self-excited oscillator, this hybrid oscillator exhibits higher sensitivity to external excitation and strong nonlinear terms. By adjusting the system parameters, the peak value of the chaos threshold can be controlled to avoid the occurrence of chaos. Based on the subharmonic Melnikov method, the subharmonic bifurcations of the system are examined and the extreme case is discussed. Some nonlinear phenomena are discovered. The system only exhibits chaotic behavior when there is a strong resonance, that is, when there is an integer-order subharmonic bifurcation. Furthermore, we find the pathways to chaos though subharmonic bifurcations encompass two distinct mechanisms: odd and even finite bifurcation sequences. The numerical simulation serves to verify the findings of the preceding analysis, while simultaneously elucidating a number of additional dynamic phenomena, including multi-stable state motion, bursting oscillations, and the coexistence of attractors.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 427-453"},"PeriodicalIF":4.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143269203","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 : 2025-01-04DOI: 10.1016/j.matcom.2024.12.025
Zhihong Zhao, Yuwei Shen
Cannibalism is a common intraspecific interaction phenomenon and thus the elucidation of the mechanisms of cannibalism can enrich the ecological dynamics. In this paper, we investigate a Holling-Tanner system with predator cannibalism, which is rarely studied. For the non-spatial system, the local dynamics of the origin are fully characterized. The global dynamics of the constant positive steady state, including global stability, Hopf bifurcation and its directions, are examined. For the diffusion system, the Turing instability and global asymptotic stability for the constant steady state are derived, and the existence of Hopf bifurcation and Turing–Hopf bifurcation are studied. We found that predator cannibalism not only leads to complex dynamical behaviors around the origin in non-spatial system, but influences the global asymptotically stability and Turing instability of , as well as results in Hopf bifurcation and Turing–Hopf bifurcation of diffusion system, which can reveal the reasons for the effects of predator cannibalism on biological systems. The numerical verification of the obtained results, the evaluation of the impact of predator cannibalism on the dynamics are also presented.
{"title":"Dynamic complexity of Holling-Tanner predator–prey system with predator cannibalism","authors":"Zhihong Zhao, Yuwei Shen","doi":"10.1016/j.matcom.2024.12.025","DOIUrl":"10.1016/j.matcom.2024.12.025","url":null,"abstract":"<div><div>Cannibalism is a common intraspecific interaction phenomenon and thus the elucidation of the mechanisms of cannibalism can enrich the ecological dynamics. In this paper, we investigate a Holling-Tanner system with predator cannibalism, which is rarely studied. For the non-spatial system, the local dynamics of the origin are fully characterized. The global dynamics of the constant positive steady state, including global stability, Hopf bifurcation and its directions, are examined. For the diffusion system, the Turing instability and global asymptotic stability for the constant steady state are derived, and the existence of Hopf bifurcation and Turing–Hopf bifurcation are studied. We found that predator cannibalism not only leads to complex dynamical behaviors around the origin in non-spatial system, but influences the global asymptotically stability and Turing instability of <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>, as well as results in Hopf bifurcation and Turing–Hopf bifurcation of diffusion system, which can reveal the reasons for the effects of predator cannibalism on biological systems. The numerical verification of the obtained results, the evaluation of the impact of predator cannibalism on the dynamics are also presented.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 227-244"},"PeriodicalIF":4.4,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143367926","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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