A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The ...A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.展开更多
In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we ...In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.展开更多
In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there...In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.展开更多
A stage-structured prey-predator model with time delay and harvesting is considered.Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria.Moreover,t...A stage-structured prey-predator model with time delay and harvesting is considered.Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria.Moreover,the existence of a Hopf bifurcation at the coexistence equilibrium is established.Finally,the optimal harvesting problem is formulated and solved by Pontryagin’s maximum principle,and an example is given for illustration.展开更多
Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the i...Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.展开更多
In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence o...In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.展开更多
A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the gr...A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.展开更多
Intercalation provides to the host materials a means for controlled variation of many physical/chemical properties and dominates the reactions in metal‐ion batteries.Of particular interest is the graphite intercalati...Intercalation provides to the host materials a means for controlled variation of many physical/chemical properties and dominates the reactions in metal‐ion batteries.Of particular interest is the graphite intercalation compounds with intriguing staging structures,which however are still unclear,especially in their nanostructure and dynamic transition mechanism.Herein,the nature of the staging structure and evolution of the lithium(Li)‐intercalated graphite was revealed by cryogenic‐transmission electron microscopy and other methods at the nanoscale.The intercalated Li‐ions distribute unevenly,generating local stress and dislocations in the graphitic structure.Each staging compound is found macroscopically ordered but microscopically inhomogeneous,exhibiting a localized‐domains structural model.Our findings uncover the correlation between the long‐range ordered structure and short‐range domains,refresh the insights on the staging structure and transition of Li‐intercalated/deintercalated graphite,and provide effective ways to enhance the reaction kinetic in rechargeable batteries by defect engineering.展开更多
A Holling type III predator-prey model with stage structure for prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discus...A Holling type III predator-prey model with stage structure for prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the uniformly persistence theory, the system is proven to be permanent if the coexistence equilibrium exists. By using Lyapunov functionals and La Salle's invariance principle, it is shown that the two boundary equilibria is globally asymptotically stable when the coexistence equilibrium is not feasible. By using compound matrix theory, the sufficient conditions are obtained for the global stability of the coexistence equilibrium. At last, numerical simulations are carried out to illustrate the main results.展开更多
We investigate a diffusive,stage-structured epidemic model with the maturation delay and freelymoving delay.Choosing delays and diffusive rates as bifurcation parameters,the only possible way to destabilize the endemi...We investigate a diffusive,stage-structured epidemic model with the maturation delay and freelymoving delay.Choosing delays and diffusive rates as bifurcation parameters,the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation.The normal forms of Hopf bifurcations on the center manifold are calculated,and explicit formulae determining the criticality of bifurcations are derived.There are two different kinds of stable oscillations near the first bifurcation:on one hand,we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large,the first branch of Hopf bifurcating solutions is always spatially homogeneous;on the other,fixing this diffusion rate at an appropriate size,stable oscillations with different spatial profiles are observed,and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point.These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.展开更多
文摘A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.
基金This work is supported by the National Natural Science Foundation of China(Nos.12001090,11871473)Shandong Provincial Natural Science Foundation(No.ZR2019MA010)the Fundamental Research Funds for the Central Universities of China(No.2412020QD024).
文摘In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.
基金This research was partially supported by tlie National Natural Science Foundation of China(11871231,11,526095).
文摘In this paper,we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure.Using the theory of generalized saddle-point behaviors,it is shown that there exists a C1-separatrixΓon its state space such that Species 2 wins the competition whenever the initial distribution is aboveΓ,while Species 1 wins the competition whenever the initial distribution is belowΓ.Combining with the previous conclusions of the system,we give a complete classification for global competitive dynamics.Furthermore,we carefully analyze the changes of the competition outcome after introducing the stage structure.Finally,some numerical simulations are provided to illustrate the effectiveness of the theoretical results.
基金supported by the National Natural Science Foundation of China[NSFC,grant number 61261044].
文摘A stage-structured prey-predator model with time delay and harvesting is considered.Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria.Moreover,the existence of a Hopf bifurcation at the coexistence equilibrium is established.Finally,the optimal harvesting problem is formulated and solved by Pontryagin’s maximum principle,and an example is given for illustration.
基金supported partially by U.S.National Science Foundation grant DMS-0931213
文摘Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.
基金Supported by the Basis and Frontier Science Research Foundation of Henan Province (072300410096)the Natural Science Foundation of Education Department of Henan Province (2009A110023)the Youth Foundation of Zhoukou Normal University
文摘In this paper,a delayed two-species predator-prey system with stage structure and diffiusion is investigated. Based on the continuation theorem of coincidence degree theory,the suficient conditions for the existence of positive ω-periodic solution to the system are derived. The numerical simulation of an example verifies our main result.
基金This work was supported by the National Natural Science Foundation of China (No.10572011).
文摘A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.
基金support from the National Natural Science Foundation of China(NSFC nos.52172257,22005334,21773301 and 52022106)the Natural Science Foundation of Beijing(grant no.Z200013).
文摘Intercalation provides to the host materials a means for controlled variation of many physical/chemical properties and dominates the reactions in metal‐ion batteries.Of particular interest is the graphite intercalation compounds with intriguing staging structures,which however are still unclear,especially in their nanostructure and dynamic transition mechanism.Herein,the nature of the staging structure and evolution of the lithium(Li)‐intercalated graphite was revealed by cryogenic‐transmission electron microscopy and other methods at the nanoscale.The intercalated Li‐ions distribute unevenly,generating local stress and dislocations in the graphitic structure.Each staging compound is found macroscopically ordered but microscopically inhomogeneous,exhibiting a localized‐domains structural model.Our findings uncover the correlation between the long‐range ordered structure and short‐range domains,refresh the insights on the staging structure and transition of Li‐intercalated/deintercalated graphite,and provide effective ways to enhance the reaction kinetic in rechargeable batteries by defect engineering.
基金Supported by the NSFC(11371368)Supported by the Basic Courses Department of OEC Foundation(Jcky1302)
文摘A Holling type III predator-prey model with stage structure for prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the uniformly persistence theory, the system is proven to be permanent if the coexistence equilibrium exists. By using Lyapunov functionals and La Salle's invariance principle, it is shown that the two boundary equilibria is globally asymptotically stable when the coexistence equilibrium is not feasible. By using compound matrix theory, the sufficient conditions are obtained for the global stability of the coexistence equilibrium. At last, numerical simulations are carried out to illustrate the main results.
基金supported by National Natural Science Foundation of China(No.11901369,No.61872227,No.12071268 and No.11771109)Natural Science Basic Research Plan in Shaanxi Province of China(grant No.2020JQ-699)Shandong Provincial Natural Science Foundation(No.ZR2019QA020)。
文摘We investigate a diffusive,stage-structured epidemic model with the maturation delay and freelymoving delay.Choosing delays and diffusive rates as bifurcation parameters,the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation.The normal forms of Hopf bifurcations on the center manifold are calculated,and explicit formulae determining the criticality of bifurcations are derived.There are two different kinds of stable oscillations near the first bifurcation:on one hand,we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large,the first branch of Hopf bifurcating solutions is always spatially homogeneous;on the other,fixing this diffusion rate at an appropriate size,stable oscillations with different spatial profiles are observed,and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point.These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.
