THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

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.

Qualitative Properties of Equilibrium Point in a Discrete Predator-Prey Model

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.

Dynamic Analysis of a Predator-Prey Model with Holling-II Functional Response

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.

Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

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.

基于Predator-Prey行为的双种群粒子群优化算法

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.

一类相异功能反应的predator-prey扩散系统的稳定性

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.

Note on a diffusive ratio-dependent predator-prey model

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.

ON A MULTI-DELAY LOTKA-VOLTERRA PREDATOR-PREY MODEL WITH FEEDBACK CONTROLS AND PREY DIFFUSION

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.

具有无限时滞离散的Predator-Prey系统周期正解的存在性

研究了具有三个物种周期的Predator-Prey差分模型,用拓扑度理论讨论了具有无限时滞差分系统的周期正解的存在性,证明了具有无限时滞差分系统的正周期解存在的充分条件为:(ⅰ) r1 a32- r3 a12exp(2 r2ω)>0;(ⅱ) r1 a32- r3 a12exp(2 r2ω)- r2 a11 a32exp(2 r1ω)<0;(ⅲ)- a32 a12 r1+ a32 a11 r2+ a21 a12 r3<0.

Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems

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.

PERSISTENCE AND THE GLOBAL DYNAMICS OF THE POSITIVE SOLUTIONS FOR A RATIODEPENDENT PREDATOR-PREY SYSTEM WITH A CROWDING TERM IN THE PREY EQUATION

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.

Permanence and Global Stability for a Non-Autonomous Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes with Delays

In this paper, a nonautonomous predator-prey system based on a modified version of the Leslie-Gower scheme and Holling-type II scheme with delayed effect is investigated. The general criteria of integrable form on the permanence are established. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solutions to the

POSITIVE STEADY STATES OF A DIFFUSIVE PREDATOR-PREY SYSTEM WITH PREDATOR CANNIBALISM

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.

The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and Allee Effect

In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.

STABILITY OF A PREDATOR-PREY SYSTEM WITH PREY TAXIS IN A GENERAL CLASS OF FUNCTIONAL RESPONSES

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.

Control problems of an age-dependentpredator-prey system

This paper is concerned with optimal harvesting problems for a system consisting oftwo populations with age-structure and interaction of predator-prey. Existence and uniquenessof non-negative solutions to the system and the continuous dependence of solutions on controlvariables are investigated. Existence of optimal policy is discussed, optimality conditions arederived by means of normal cone and adjoint system techniques.

The Dynamical Behavior of a Certain Predator-Prey System with Holling Type II Functional Response

In this paper we analytically and numerically consider the dynamical behavior of a certain predator-prey system with Holling type II functional response, including local and global stability analysis, existence of limit cycles, transcritical and Hopf bifurcations. Mathematical theory derivation mainly focuses on the existence and stability of equilibrium point as well as threshold conditions for transcritical and Hopf bifurcation, which can in turn provide a theoretical support for numerical simulation. Numerical analysis indicates that theoretical derivation results are correct and feasible. In addition, it is successful to show that the dynamical behavior of this predator-prey system mainly depends on some critical parameters and mathematical relationships. All these results are expected to be meaningful in the study of the dynamic complexity of predatory ecosystem.

Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response

In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j &#8800;0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.

PERSISTENCE IN A THREE SPECIES LOTKA-VOLTERRA NONPERIODIC PREDATOR-PREY SYSTEM

The predator-prey model for three species in which the right-hand sides are nonperiodic functions in time were considered, It's proved that the model is persistent under appropriate conditions.