Delayed stage-structured predator-prey model with impulsive perturbations on predator and chemical control on prey

We consider a delayed stage-structured pest management predator-prey system with impulsive transmitting on predator and chemical control on prey. Sufficient conditions of the global attractiveness of the pest-extinction boundary periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for practical pest management.

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.

Dynamic Behavior of a Predator-prey System with Stage-structure for Prey

In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.

A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects

A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

A Stage-structured Three-species Model with Intra-guild Predation and Disturbing Pulse

This paper considers a stage-structured three species model with intra-guild predation and disturbing pulse. Sufficient conditions which guarantee the global attractivity of boundary periodic solution and permanence of the system are obtained. Our results show that the pulse and time delay bring great effect on the dynamical behaviors of the model.

Global Stability of A Stochastic Predator-prey Model with Stage-structure

In this paper, a stochastic predator-prey model with stage structure for predatorand ratio-dependent functional response is concerned. Sufficient conditions for the globalasymptotic stability of positive equilibrium are established. Some numerical simulations arecarried out to illustrate the theoretical results.

Existence of Periodic Solution for a Non-Autonomous Stage-Structured Predator-Prey System with Impulsive Effects

In this paper, we studied a non-autonomous predator-prey system where the prey dispersal in a two-patch environment. With the help of a continuation theorem based on coincidence degree theory, we establish sufficient conditions for the existence of positive periodic solutions. Finally, we give numerical analysis to show the effectiveness of our theoretical results.

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.

A delayed stage-structure brucellosis model with interaction among seasonality, time-varying incubation and density-dependent growth

In this paper,a class of brucellosis transmission model with seasonal alternation,density-dependent growth,stage-structure,maturation delay,time-varying incubation is established.The basic reproduction number Ro is derived,by which we find that the brucellosis is uniformly persistent if R_(0)>1,while the disease-free periodic solution is globally attractive if R_(0)<1.The theoretical results are illustrated by numerical simulation,from which we find that the brucellosis transmission would be overestimated(or underestimated)if we ignore the influence of time-varying incubation or maturation delay.If density-dependent growth of animals is ignored,the risk of brucellosis may be far underestimated,the extinction of brucellosis can be obtained by numerical simulation under the same conditions.Seasonality significantly affects the long-term dynamic behavior of brucellosis,and the inconsistency of parameter periods results in complex dynamic behavior.

Dynamics of a Delayed Predator-prey System with Stage Structure for Predator and Prey

In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally~ numerical simulations are presented to support the theoreticM analysis.

Dynamics of a delay-induced prey-predator system with interaction between immature prey and predators

In biological pest control systems,several pests(including insects,mites,weeds,etc.)are controlled by biocontrol agents that rely primarily on predation.Following this biocontrol management ecology,we have created a three-tier prey-predator model with prey phase structure and predator gestation delay.Several studies have demonstrated that predators with Holling type-II functional responses sometimes consume immature prey.A study of the well-posedness and local bifurcation(such as saddle-node and transcritical)near the trivial and planer equilibrium points is carried out.Without any time lag,the prey development coeficient has a stabilizing impact,while increasing attack rate accelerates instability.Energy transformation rate and handling time are shown to cause multiple stability switches in the system.Numerical results demonstrate time delay is the key destabilizer that destroys stability.Our model can replicate more realistic events by including time-dependent factors and exploring the dynamic behavior of nonautonomous systems.In the presence of time delay,sufficient conditions of permanence and global attractivity of the nonautonomous system are derived.Finally,MATLAB simulations are performed to validate the analytical findings.

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.

A DELAYED RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURED AND IMPULSIVE EFFECT

In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These＇ results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable. Key words Globally attractivity, impulsive effect, permanence, ratio-dependent, stage-structured.

The Analysis of Model on Population Growth with Stage-structure in the Polluted Environment

In this paper, the authors considered a single-species model with stage-structure in a polluted ecological environment. Subject to the outside toxin input quantity being stable, the authors established the sufficient conditions under which the species will be permanent using Lyapunov method. At the same time biological implications briefly of these results are discussed.

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.

A NONAUTONOMOUS STAGE-STRUCTURED SINGLE SPECIES MODEL WITH DIFFUSION

A stage-structured single species model with diffusion is constructed and is considered, in which the coefficients are time dependent. It is shown that under some appropriate assumptions, the system is persistent. Criteria for the existence and uniqueness of the periodic and almost periodic positive solutions are also given. Further, the stability of almost periodic solution under the disturbances from the hull are discussed.

ATTRACTING BEHAVIOR OF INSHORE-OFFSHORE FISHING MODEL WITH STAGE-STRUCTURE

This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.

Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment

In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population- extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.

The Effect of Dispersal on Population Growth with Stage-structure

The effect of dispersal on the permanence of population in a polluted patch is studied in this paper. The authors constructed a single-species dispersal model with stage-structure in two patches. The analysis focuses on the case that the toxicant input in the polluted patch has a limit value. The authors derived the conditions under which the population will be either permanent, or extinct.

A STAGE-STRUCTURED AND HARVESTING PREDATOR-PREY SYSTEM

A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out to illustrate the validity of our results.