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THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT
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作者 赵敏 袁荣 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期1096-1114,共19页
In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or ext... In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case. 展开更多
关键词 predator-prey system PERSISTENCE nonlocal dispersal shifting environment
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Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model
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作者 Weijie Lin Minhong Yang +2 位作者 Chenhao Sun Kaiwen Guan Xiaoliang Zhou 《Journal of Applied Mathematics and Physics》 2024年第8期2920-2927,共8页
In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic S... In this paper, the dynamic properties of a discrete predator-prey model are discussed. The properties of non-hyperbolic fixed points and hyperbolic fixed points of the model are analyzed. First, by using the classic Shengjin formula, we find the existence conditions for fixed points of the model. Then, by using the qualitative theory of ordinary differential equations and matrix theory we indicate which points are hyperbolic and which are non-hyperbolic and the associated conditions. 展开更多
关键词 Discrete predator-prey Model Non-Hyperbolic Fixed Point NODE Saddle Point
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SOlvaBILITY OF HIGHER INDEX TIME-VARYING LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS 被引量:1
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作者 宋永忠 《Acta Mathematica Scientia》 SCIE CSCD 2001年第1期77-92,共16页
Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some eq... Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed. 展开更多
关键词 differential-algebraic equations INDEX SOLVABILITY EXISTENCE UNIQUENESS
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DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY 被引量:1
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作者 WANG Lin-xiang Roderick V. N. Melnik 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第9期1185-1196,共12页
An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction... An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case. 展开更多
关键词 THERMOELASTICITY TWO-DIMENSIONAL differential-algebraic solvers
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A Class of Parallel Runge-Kutta Methods for Differential-Algebraic Systems of Index 2
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作者 Fei Jinggao(Beijing Institute of Computer Application and Simulation Technology, 100854, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1999年第3期64-75,共12页
A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such m... A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods. 展开更多
关键词 MULTIPROCESSOR SYSTEM PARALLEL algorithm Runges-Kutta method differential-algebraic SYSTEM
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Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides
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作者 LengXin SongXiaoqiu LiuDegui 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第1期173-178,共6页
Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosen... Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS). 展开更多
关键词 ALGORITHM differential-algebraic systems right-hand sides typical discontinuous parts.
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Stability of Nonlinear Differential-Algebraic Systems Via Additive Identity
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作者 Pierluigi Di Franco Giordano Scarciotti Alessandro Astolfi 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第4期929-941,共13页
The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Di... The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory. 展开更多
关键词 differential-algebraic systems Lyapunov method small-gain theorem stability analysis
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ON A REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH PROPERLY STATED LEADING TERM
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作者 刘红 宋永忠 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期383-398,共16页
In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]' + B(t)x(t) = q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular inde... In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]' + B(t)x(t) = q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given. 展开更多
关键词 differential-algebraic equations (DAEs) properly stated leading term in-dex REGULARIZATION
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NONNEGATIVITY OF SOLUTIONS OF NONLINEAR FRACTIONAL DIFFERENTIAL-ALGEBRAIC EQUATIONS
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作者 Xiaoli DING Yaolin JIANG 《Acta Mathematica Scientia》 SCIE CSCD 2018年第3期756-768,共13页
Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As... Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method. 展开更多
关键词 Fractional differential-algebraic equations nonnegativity of solutions waveform relaxation monotone convergence
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Delay and Its Time-Derivative Dependent Stable Criterion for Differential-Algebraic Systems
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作者 Hui Liu Yucai Ding 《Applied Mathematics》 2016年第10期1124-1133,共10页
In this paper, the stable problem for differential-algebraic systems is investigated by a convex op-timization approach. Based on the Lyapunov functional method and the delay partitioning approach, some delay and its ... In this paper, the stable problem for differential-algebraic systems is investigated by a convex op-timization approach. Based on the Lyapunov functional method and the delay partitioning approach, some delay and its time-derivative dependent stable criteria are obtained and formulated in the form of simple linear matrix inequalities (LMIs). The obtained criteria are dependent on the sizes of delay and its time-derivative and are less conservative than those produced by previous approaches. 展开更多
关键词 differential-algebraic Systems Stability Analysis Lyapunov-Krasovskii Functional Delay Partitioning Approach Linear Matrix Inequality (LMI)
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Dynamic Analysis of a Predator-Prey Model with Holling-II Functional Response
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作者 Jiemin Mo Wanying Li +2 位作者 Donghuan He Songbo Wang Xiaoliang Zhou 《Journal of Applied Mathematics and Physics》 2023年第10期2871-2878,共8页
A predator-prey model with linear capture term Holling-II functional response was studied by using differential equation theory. The existence and the stabilities of non-negative equilibrium points of the model were d... A predator-prey model with linear capture term Holling-II functional response was studied by using differential equation theory. The existence and the stabilities of non-negative equilibrium points of the model were discussed. The results show that under certain limited conditions, these two groups can maintain a balanced position, which provides a theoretical reference for relevant departments to make decisions on ecological protection. 展开更多
关键词 predator-prey Model Holling-II Functional Response Equilibrium Point STABILITY
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Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System
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作者 Mingxia Duan Jiying Ma 《Open Journal of Applied Sciences》 CAS 2023年第3期396-413,共18页
In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation a... In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method. 展开更多
关键词 Discrete-Time predator-prey System Ratio-Dependent Functional Response Stability and Bifurcation Analysis
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基于Predator-Prey行为的双种群粒子群优化算法 被引量:2
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作者 秦全德 牛奔 +1 位作者 李丽 李荣钧 《信息与控制》 CSCD 北大核心 2011年第6期733-739,共7页
根据生物的捕食-食饵(predator-prey)行为的规律,提出了一种双种群粒子群优化(DPPSO)算法.将粒子分成predator和prey两个种群,其中predator种群每间隔一定的迭代次数后排斥prey种群.在排斥的过程中,predator种群采用"擒贼先擒王&qu... 根据生物的捕食-食饵(predator-prey)行为的规律,提出了一种双种群粒子群优化(DPPSO)算法.将粒子分成predator和prey两个种群,其中predator种群每间隔一定的迭代次数后排斥prey种群.在排斥的过程中,predator种群采用"擒贼先擒王"的策略,逐步向prey种群的群体最优位置靠近,同时每个prey粒子尽量逃离距离最近的predator粒子.采用了一种速度变异的方法提高prey种群在停滞状态时摆脱局部最优的能力.基准函数的仿真结果表明DPPSO具有速度收敛快和全局搜索能力强的特点. 展开更多
关键词 粒子群优化 predator-prey行为 双种群 基准函数
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一类相异功能反应的predator-prey扩散系统的稳定性 被引量:1
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作者 郑唯唯 贺松梅 罗立贵 《西安工程大学学报》 CAS 2010年第4期530-534,共5页
针对斑块生境下具有庇护所效应的相异功能性反应predator-prey扩散系统,讨论了系统持续生存的条件.运用常微分方程定性理论讨论了系统解的有界性,通过构造Lyapunov函数得到了一定条件下该系统正解是全局渐近稳定的.进一步利用Pioncare... 针对斑块生境下具有庇护所效应的相异功能性反应predator-prey扩散系统,讨论了系统持续生存的条件.运用常微分方程定性理论讨论了系统解的有界性,通过构造Lyapunov函数得到了一定条件下该系统正解是全局渐近稳定的.进一步利用Pioncare定理和Brower定理证明了惟一周期正解的存在性与稳定性. 展开更多
关键词 predator-prey扩散系统 稳定性 功能反应 庇护所效应
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A multiscale differential-algebraic neural network-based method for learning dynamical systems
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作者 Yin Huang Jieyu Ding 《International Journal of Mechanical System Dynamics》 EI 2024年第1期77-87,共11页
The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in componen... The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions. 展开更多
关键词 dynamical systems learning multibody system dynamics differential-algebraic equation neural networks multiscale structures
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具有食饵避难所的离散捕食者-食饵模型的余维二分支分析
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作者 庞茹一 陈巧玲 《Chinese Quarterly Journal of Mathematics》 2024年第2期128-143,共16页
In this paper,a discrete predator-prey model with prey refuge is investigated.It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances.The bifurcation diagrams and phase ... In this paper,a discrete predator-prey model with prey refuge is investigated.It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances.The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors,such as limit cycle,periodic solutions,chaos and codimension-1 bifurcations. 展开更多
关键词 REFUGE Discrete predator-prey model Codimension-2 bifurcations CHAOS
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Note on a diffusive ratio-dependent predator-prey model
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作者 陈滨 许志奋 《Journal of Southeast University(English Edition)》 EI CAS 2006年第2期294-296,共3页
Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady s... Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective. 展开更多
关键词 ratio-dependent predator-prey model global stability comparison principle ITERATION
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Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems 被引量:4
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作者 莫嘉琪 韩祥临 《Journal of Zhejiang University Science》 CSCD 2003年第5期511-513,共3页
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh... The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems. 展开更多
关键词 NONLINEAR predator-prey Reaction diffusion Singular perturbation
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ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION 被引量:3
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作者 Changyou WANG Nan LI +2 位作者 Yuqian ZHOU Xingcheng PU Rui LI 《Acta Mathematica Scientia》 SCIE CSCD 2019年第2期429-448,共20页
This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as co... This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive solution for the predator-prey system.Furthermore, some conditions for the existence, uniqueness and stability of positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis techniques. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria are new, general, and easily verifiable. Finally, we still solve numerically the corresponding stochastic predator-prey models with multiplicative noise sources, and obtain some new interesting dynamical behaviors of the system. 展开更多
关键词 predator-prey model: delay diffusion: PERMANENCE ATTRACTIVITY periodic solution
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PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION 被引量:3
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作者 曾宪忠 顾永耕 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期689-703,共15页
This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coeffici... This paper deals with the global dynamical behaviors of the positive solutions for a parabolic type ratio-dependent predator-prey system with a crowding term in the prey equation, where it is assumed that the coefficient of the functional response is less than the coefficient of the intrinsic growth rates of the prey species. We demonstrated some special dynamical behaviors of the positive solutions of this system which the persistence of the coexistence of two species can be obtained when the crowding region in the prey equation only is designed suitably. Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable. 展开更多
关键词 ratio-dependent predator-prey system crowding effect PERSISTENCE global stability
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