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

On the Permanence of a Nonautonomous Nicholson’s Blowflies Model with Feedback Control and Delay

A nonautonomous Nicholson's Blowflies model with feedback control and delay is investigated in this paper. We show that for this system, feedback control variable has no influence on the persistent property of the system.

Permanence and periodic solutions of delayed predator-prey system with impulse

The existence of positive periodic solution of a generalized semi-ratio-dependent predator-prey system with time delay and impulse is studied by using the continuation theorem based on the coincidence degree theory. The permanence of the system is also considered. The results partially improve and extend some known criteria.

Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey

We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.

PERMANENCE AND ASYMPTOTIC PROPERTIES OF NONLINEAR DELAY DIFFERENCE EQUATIONS

The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.

Partial extinction, permanence and global attractivity innonautonomous n-species Lotka-Volterra competitivesystems with impulses

In this paper, the qualitative properties of general nonautonomous Lotka-Volterran-species competitive systems with impulsive e？ects are studied. Some new criteria on thepermanence, extinction and global attractivity of partial species are established by used themethods of inequalities estimate and Liapunov functions. As applications, nonautonomous twospecies Lotka-Volterra systems with impulses are discussed.

Permanence and Positive Periodic Solutions for Kolmogorov Competing Species Systems with Periodic Forced Terms

In this paper，we consider the Kolmogorov type n-species competition systems with forced terms．We prove that this system is permanent in the case of which there are positive forced terms in this system;and if there are several negative forced terms in this system，it has at least two positive periodic solutions.

The permanence of a higher order discrete time system

The permanence of a nonlinear higher order discrete time system from macroeconomics is studied, and a sufficient condition is proposed for the permanence of the system described by 11(,...,)nnnnkxrxfxx---=+ where :kfRR, the initial values 01,,kxx-are real numbers and [0,1)r is constant after exploring the relationship between this equation and 1(,...,)nnnkxfxx--= for certain classes of function f. As an application a short proof is given to a known result in a simpler way than ever reported.

PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS

In this article, the permanence and persistence for thrce classes time varying Lotka-Volterra ecological system are investigated by using Lyapunov stability analysis and constrncting the compact set of attraction. Some examples are given to illustrate the theorems.

Permanence of a Nicholson's Blowflies Model with Feedback Control and Multiple Time-varying Delays

This paper covers the dynamic behaviors for a class of Nicholson’s blowflies model with multiple time-varying delay and feedback control. By using the dierential inequality theory, a set of sucient conditions are obtained to ensure the permanence of the system. Our result shows that feedback control variables have no influence on the permanence of the system.

Permanence, Periodicity and Extinction of a Delayed Biological System with Stage-Structured Preference for Predator

This study considers a delayed biological system of predator-prey interactions where the predator has stage-structured preference. It is assumed that the prey population has two stages: immature and mature. The predator population has different preference for the stage-structured prey. This type of behavior has been reported in Asecodes hispinarum and Microplitis mediator. By some lemmas and methods of delay differential equation, the conditions for the permanence, existence of positive periodic solution and extinction of the system are obtained. Numerical simulations are presented that illustrate the analytical results as well as demonstrate certain biological phenomena. In particular, overcrowding of the predator does not affect the persistence of the system, but our numerical simulations suggest that overcrowding reduces the density of the predator. Under the assumption that immature prey is easier to capture, our simulations suggest that the predator’s preference for immature prey increases the predator density.

PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.

Permanence and Global Attractivity of a Discrete Semi-Ratio-Dependent Predator-Prey System with Holling Ⅳ Type Functional Response

In this paper, we investigate a discrete semi-ratio dependent predator-prey system with Holling IV type functional response. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained. Meanwhile, we discuss the existence of the positive periodic solution and global stability of the system.

PERMANENCE AND PERIODIC SOLUTION FOR NONAUTONOMOUS COMPETITION-PREDATOR SYSTEM WITH TYPE II FUNCTIONAL RESPONSE

A nonautonomous multispecies competition-predator system with type Ⅱfunctional response is studied in this paper. It is proved that the system is per-manent under some appropriate conditions. Further, if the system is a periodic one, a set of easily verifiable suflficient conditions which guarantee the existence, uniqueness and global attractivity of a strictly positive periodic solution are ob-tained.

PERMANENCE AND GLOBAL ATTRACTIVITY OF N-SPECIES COOPERATION SYSTEM WITH DISCRETE TIME DELAYS AND FEEDBACK CONTROLS

In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.

PERMANENCE OF A NONLINEAR PERIODIC PREDATOR-PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENCE

In this paper,a set of suffcient conditions which ensure the permanence of a nonlinear periodic predator-prey system with prey dispersal and predator density-independence are obtained,where the prey species can disperse among n patches,while the density-independent predator is confined to one of the patches and cannot disperse. Our results generalize some known results.

PERMANENCE OF A PERIODIC PREDATOR-PREY SYSTEM WITH GENERAL HOLLING TYPE FUNCTIONAL RESPONSE AND STAGE STRUCTURE FOR PREY

In this paper, we give some sufficient and necessary condition of permanence for a periodic predator-prey system with general Holling type functional response and stage structure for preys. By doing this, we improve some known results.

PERMANENCE AND GLOBAL STABILITY OF A FEEDBACK CONTROL SYSTEM WITH DELAYS

This paper considers a feedback control systems of differential equations with delays. By applying the differential inequality theorem, sufficient conditions for the permanence of the system are obtained. Also, by constructing a suitable Lyapunov functional, a criterion for the global stability of the model is obtained.

Permanence of a diffusive Leslie-Gower predator-prey model incorporating a prey refuge

The diffusive Leslie-Clower predator-prey model incorporating a prey refuge is recon- sidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones.

PERMANENCE AND PERIODIC SOLUTION OF NONAUTONOMOUS DELAY LOTKA-VOLTERRA DIFFUSION SYSTEM

This paper analyzes permanence, existence and global attractivity of positiveperiodic solution in nonautonomous delay diffusive Lotka-Volterra competitive system fora patchstyle environment, by applying the invariant rectangle and Lyapunov functional.