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-extincti...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.展开更多
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 o...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.展开更多
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 stag...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.展开更多
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 o...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.展开更多
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 ...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.展开更多
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 predat...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.展开更多
Vegetables are rich in vitamins,minerals and dietary fibers.Insects attack vegetable crops and to control them,farmers spray chemical insecticides.However,the continuous insecticide spray leads to residues in vegetabl...Vegetables are rich in vitamins,minerals and dietary fibers.Insects attack vegetable crops and to control them,farmers spray chemical insecticides.However,the continuous insecticide spray leads to residues in vegetables and harms the beneficial insects.In this research work,we formulate a novel stage-structured insect-vegetable crop interaction model to investigate the effects of a one-time insecticide spray and external efforts on vegetable production and insect population.This study determines the threshold values of the maturation period and immature insect abatement rate above which the insectfree equilibrium becomes stable,while the feasibility of the interior equilibrium ceases.Furthermore,we demonstrate that insects with a short maturation period can also be controlled by increasing the abatement rates of both immature and mature insects.The global stability of the insect-free equilibrium is discussed,and the effects of key parameters on vegetable production are analyzed.Numerical simulation is also presented to substantiate the theoretical results.Our research indicates that attaining the targeted vegetable yield necessitates a critical emphasis on managing insecticide abatement rates,along with the effective implementation of external efforts.展开更多
Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are inves...Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are investigated theoretically and graphically.First,stability charts and rightmost characteristic roots of the positive equilibrium are elucidated analytically and numerically.Furthermore,the Hopf bifurcation at the positive equilibrium is derived employing geometric stability switch criterion.Second,the properties of Hopf bifurcation are determined using the center manifold theorem and by reducing the equation to the Poincarénormal form.Finally,the correctness of the theoretical derivation is confirmed using a numerical simulation based on specific parameter values.Our results show that with an increase in delay T,the unique positive equilibrium may undergo two stability switches:from stable to unstable,and from unstable to stable.Interestingly,the characteristic equation has pure imaginary roots at the second pair and subsequent critical values,However,Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts,except the pure imaginary roots.We also simulate the unstable periodic solutions at the second pair of critical values through a bifurcation diagram.Therefore,a pair of supercritical Hopf bifurcations appear around the positive equilibrium of the housefly population stage-structured model.展开更多
A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By...A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.展开更多
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 equilib...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.展开更多
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 a...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.展开更多
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 conditio...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.展开更多
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 t...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.展开更多
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. Cri...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.展开更多
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 ultima...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.展开更多
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 ana...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.展开更多
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 ...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.展开更多
In this paper, a stage-structured predator prey system with birth pulse and disturbed time delay is investigated. The conditions of the prey-extinction periodic solution of the system which are globally attractive hav...In this paper, a stage-structured predator prey system with birth pulse and disturbed time delay is investigated. The conditions of the prey-extinction periodic solution of the system which are globally attractive have been obtained. Furthermore, the sufficient corlditions for the permanence of the system are established. Finally, numerical analysis is given to confirm the theoretical results.展开更多
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 de...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.展开更多
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 ...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.展开更多
基金the National Natural Science Foundation of China(No.10471117)the Leading Academic Discipline Project of Guizhou Province
文摘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.
基金the National Natural Science Foundation of China(No.10771179)the Emphasis Subject of Guizhou Province of China
文摘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.
基金Foundation item： Supported by the NNSF of China（11071254） Supported by the Science Foundation of Mechanical Engineering College（YJJXMll004）
文摘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.
基金Foundation item： Supported by the National Natural Science Foundation of China（10771179）
文摘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.
文摘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.
文摘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.
文摘Vegetables are rich in vitamins,minerals and dietary fibers.Insects attack vegetable crops and to control them,farmers spray chemical insecticides.However,the continuous insecticide spray leads to residues in vegetables and harms the beneficial insects.In this research work,we formulate a novel stage-structured insect-vegetable crop interaction model to investigate the effects of a one-time insecticide spray and external efforts on vegetable production and insect population.This study determines the threshold values of the maturation period and immature insect abatement rate above which the insectfree equilibrium becomes stable,while the feasibility of the interior equilibrium ceases.Furthermore,we demonstrate that insects with a short maturation period can also be controlled by increasing the abatement rates of both immature and mature insects.The global stability of the insect-free equilibrium is discussed,and the effects of key parameters on vegetable production are analyzed.Numerical simulation is also presented to substantiate the theoretical results.Our research indicates that attaining the targeted vegetable yield necessitates a critical emphasis on managing insecticide abatement rates,along with the effective implementation of external efforts.
基金partially supported by the National Natural Science Foundation of China(Nos.12201271 and 12361101)the Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University.
文摘Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are investigated theoretically and graphically.First,stability charts and rightmost characteristic roots of the positive equilibrium are elucidated analytically and numerically.Furthermore,the Hopf bifurcation at the positive equilibrium is derived employing geometric stability switch criterion.Second,the properties of Hopf bifurcation are determined using the center manifold theorem and by reducing the equation to the Poincarénormal form.Finally,the correctness of the theoretical derivation is confirmed using a numerical simulation based on specific parameter values.Our results show that with an increase in delay T,the unique positive equilibrium may undergo two stability switches:from stable to unstable,and from unstable to stable.Interestingly,the characteristic equation has pure imaginary roots at the second pair and subsequent critical values,However,Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts,except the pure imaginary roots.We also simulate the unstable periodic solutions at the second pair of critical values through a bifurcation diagram.Therefore,a pair of supercritical Hopf bifurcations appear around the positive equilibrium of the housefly population stage-structured model.
基金Supported by the Social Science Foundation of Hebei Province(HB23TJO03)。
文摘A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.
文摘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.
基金Supported by the National Natural Science Foundation of China(Nos.11371368)The Natural Science Foundation of HeBei(No.A2014506015)
文摘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.
文摘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.
基金the National Natural Science Foundation of China under Grant No.10471117,10771179the Natural Science and Development Foundation of Shandong University of Science and Technology under Grant No.05g016
文摘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.
文摘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.
基金Acknowledgments The work of the first author was supported by National Natural Science Foundation of China （No. 11361014） and the project of high level creative talents in Guizhou Province （No. 20164035）. This research was supported by National Natural Science Foundation of China （Nos. 11361014, 10961008）, the Science Technology Foundation of Guizhou Education Department （No. 2008038）, and the Science Technology Foundation of Guizhou （No. 2010J2130）.
文摘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.
基金The NSF(KJ2013A003,KJ2013B137)of the Higher Education Institutions of Anhui Province
文摘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.
基金supported by the Foundation of Fujian Education Bureau (JA08253)the Technology Innovation Platform Project of Fujian Province (2009J1007)
文摘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.
文摘In this paper, a stage-structured predator prey system with birth pulse and disturbed time delay is investigated. The conditions of the prey-extinction periodic solution of the system which are globally attractive have been obtained. Furthermore, the sufficient corlditions for the permanence of the system are established. Finally, numerical analysis is given to confirm the theoretical results.
文摘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.
基金Supported by the National Science Foundation of China(No.10461002)Beijing Jiaotong University Science Foundation of China(No.2005sm063).
文摘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.
