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BOUNDEDNESS AND ASYMPTOTIC STABILITY IN A predator-prey CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS

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Acta Mathematica Scientia 2022年第3期42卷 1035-1057页

作者：邱蜀燕穆春来易红 School of Sciences Southwest Petroleum UniversityChengdu 610500China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China

This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

关键词： Chemotaxis predator-prey boundedness stabilization

Hopf bifurcation of a delayed predator-prey model with Allee effect and anti-predator behavior

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生物数学学报:英文版 2023年第7期16卷 111-139页

作者： Xinyue Xu Yan Meng Yangyang Shao School of Mathematics and Physics University of Science and Technology Beijing Beijing 100083P.R.China

This paper proposes a diffusive predator-prey model with Allee effect,time delay and anti-predator behavior.First,the existence and stability of all equilibria are analyzed and the conditions for the appearance of the Hopf bifurcation are studied.Using the normal form and center manifold theory,the formulas which can determine the direction,period and stability of Hopf bifurcation are obtained.Numerical simulations show that the Allee effect can determine the survival abundance of the prey and predator populations,and anti-predator behavior can greatly improve the stability of the coexisting equilibrium.

关键词： predator-prey Hopf bifurcation delay and diffusion Allee effect numerical simulation

Comparative study on bifurcation control methods in a fractional-order delayed predator-prey system

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Science China(Technological Sciences) 2019年第2期62卷 298-307页

作者： HUANG ChengDai CAO JinDe School of Mathematics and Statistics Xinyang Nomal University School of Mathematics and Research Center for Complex Systems and Network Sciences Southeast University School of Mathematics and Statistics Shandong Normal University

This paper focuses on the comparative analysis of bifurcation control approaches for a fractional-order delayed predator-prey system. The state feedback schemes with and without time delay are dexterously designed during the bifurcation control for the proposed system, and the comparative study is elaborately performed on bifurcation control theoretically. The salient feature of the current paper is that the analysis of time of bifurcation control for the proposed system is investigated based on various state feedback control strategies. Analysis reveals that the feedback control approach without time delay overly outmatches the one with time delay for bifurcation control in the considered systems so long as the uniform feedback gain is selected. It consumes less time to control bifurcation while utilizing the first controller in comparison with the second one. Numerical examples are ultimately employed to confirm the correctness of the theoretical results.

关键词： fractional-order time delay state feedback bifurcation control predator-prey system

ON A MULTI-DELAY LOTKA-VOLTERRA predator-prey MODEL WITH FEEDBACK CONTROLS AND prey DIFFUSION

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Acta Mathematica Scientia 2019年第2期39卷 429-448页

作者：王长有李楠周钰谦蒲兴成李锐 College of Applied Mathematics Chengdu University of Information Technology Department of Applied Mathematics Southwestern University of Finance and Economics College of Automation Chongqing University of Posts and Telecommunications

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.

关键词： predator-prey model: delay diffusion: permanence attractivity periodic solution

Biologically adaptive robust mean shift algorithm with Cauchy predator-prey BBO and space variant resolution for unmanned helicopter formation

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Science China(Information Sciences) 2014年第11期57卷 195-207页

作者： WANG XiaoHua DUAN HaiBin State Key Laboratory of Virtual Reality Technology and Systems Beihang University

Visual tracking technology can provide measurement information for unmanned helicopter formation and thus, more attention is being paid to this research area. We propose a novel mean shift(MS) algorithm that is both adaptive and robust for unmanned helicopter formation and apply it to the leading unmanned helicopter tracking. The movement of an unmanned helicopter is very flexible and changeable, which makes the tracking there of more difficulty than for common targets. In creating an algorithm that can adapt to the acceleration of the unmanned helicopter and estimates both the scale and orientation of the movement changes, we combine the traditional MS with the bio-inspired Cauchy predator-prey biogeography-based optimization(CPPBBO)evolutionary algorithm, and also the space variant resolution(SVR) mechanism of the human visual system(MS-CPPBBO-SVR). To demonstrate the effectiveness and robustness of the proposed method and justify the importance of the CPPBBO algorithm and SVR mechanism at the same time, a series of comparative experiments were carried out. The experimental results of the proposed MS-CPPBBO-SVR method are compared with other competitive tracking methods, such as MS, MS with SVR(MS-SVR), MS-SVR with several other optimization algorithms, and the robust particle filter algorithm. The experimental results demonstrate that our proposed tracking approach, MS-CPPBBO-SVR, is more adaptive, robust and efficient in target tracking than the other methods.

关键词： unmanned helicopter formation tracking mean shift biogeography-based optimization(BBO) predator-prey space variant resolution(SVR)

POSITIVE STEADY STATES OF A DIFFUSIVE predator-prey SYSTEM WITH predator CANNIBALISM

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Acta Mathematica Scientia 2017年第5期37卷 1385-1398页

作者：王彪 School of Mathematics and Statistics Xi'an Jiaotong University

The purpose of this paper is to investigate positive steady states of a diffusive predator-prey system with predator cannibalism under homogeneous Neumann boundary conditions. With the help of implicit function theorem and energy integral method, nonexistence of non-constant positive steady states of the system is obtained, whereas coexistence of non-constant positive steady states is derived from topological degree theory. The results indicate that if dispersal rate of the predator or prey is sufficiently large, there is no nonconstant positive steady states. However, under some appropriate hypotheses, if the dispersal rate of the predator is larger than some positive constant, for certain ranges of dispersal rates of the prey, there exists at least one non-constant positive steady state.

关键词： predator-prey existence and nonexistence pattern formation

STABILITY OF A predator-prey SYSTEM WITH prey TAXIS IN A GENERAL CLASS OF FUNCTIONAL RESPONSES

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Acta Mathematica Scientia 2016年第1期36卷 62-72页

作者： M.YOUSEFNEZHAD S.A.MOHAMMADI Department of Mathematical Sciences Sharif University of Technology Tehran Iran Department of Mathematics College of Sciences Yasouj University Yasouj 75918-71934 Iran

In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive constant steady state is locally and globally asymptotically stable. With an eye on the biological interpretations, a numerical simulation is performed to illustrate the feasibility of the analytical findings.

关键词： predator-prey global stability steady state Lyapunov function

Limit cycles in a generalized Gause-type predator-prey system

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Journal of Central South University of Technology 2001年第4期8卷 283-286页

作者： CHEN Hai bo,LIU Yi rong (Department of Applied Mathematics and Applied Software, Central South University, Changsha 410083, China) Department of Applied Mathematics and Applied Software Central South University Changsha China

The qualitative behavior of solutions for a generalized Gause type predator prey system was studied.A large number of biological and bioeconomic models are special cases of this system.The system was investigated in the region D={(x,y)|x>0,y>0} because of the biological meaning of the system.The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theorem of cycle field of Poincare Bendixson are efficiently employed in the research.The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.

关键词： generalized Gause-type predator-prey system boundedness periodic solution existence

On a delay ratio-dependent predator-prey system with feedback controls and shelter for the prey

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International Journal of Biomathematics 2018年第7期11卷 287-316页

作者： Changyou Wang Linrui Lit Yuqian Zhou Rui Li College of Applied Mathematics Chengdu University of Information Technology Chengdu Sichuan 610225P.R.China Basic Courses Department Institute of Disaster Prevention SanheHebei 065201P.R.China College of Automation Chongqing University of Posts and Telecommunzcations Chongqing 400065 P.R.China

In this paper,a class of three-species multi-delay Lotka-Volterra ratio-dependent predator-prey model with feedback controls and shelter for the prey is considered.A set of easily verifiable sufficient conditions which guarantees the permanence of the system and the global attractivity of positive solution for the predator-prey system are established by developing some new analysis methods and using the theory of differentim inequalities as well as constructing a suitable Lyapunov function.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 addition,some numerical solutions of the equations describing the system are given to show that 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.At the same time,the influence of the delays and shelters on the dynamics behavior of the system is also considered by solving numerically the predator-prey models.

关键词： predator-prey model feedback control delay permanence attractive periodic solution