This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertili...This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertility function is regarded as a piecewise continuous smooth function with regard to their maturation period T2.The complicated dynamic behavior is proved by integrated semigroup theory and Hopf bifurcation theorem for semilinear equations with non-dense domain.Through qualitative analysis and bifurcation study of the system,we yield that this system has a nontrivial periodic solution that bifurcates from the positive equilibrium age distribution when bifurcation parameter T passes through some critical values.Numerical simulations are also provided to illustrate theoretically analytical results.展开更多
In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed...In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.展开更多
This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no co...This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.展开更多
In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Th...In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Then,by constructing suitable upper solu-tions,we give some general conditions to ensure the linear determinacy of the minimalspeed.Finally,we provide some more precise conditions that only rely on the parametersof the system such that the linear determinacy of the minimal speed is assured.展开更多
In this paper, we investigate the global existence of nonnegative solutions of a two- species Keller-Segel model with Lotka-Volterra competitive source terms. By raising the regularity of a solution from L^1 to L^p（p...In this paper, we investigate the global existence of nonnegative solutions of a two- species Keller-Segel model with Lotka-Volterra competitive source terms. By raising the regularity of a solution from L^1 to L^p（p〉1）, the existence and uniqueness of the classical global in time solution to this chemotaxis model is proved for any chemotactic coefficients X1, X2 〉 0 when the space dimension is one. Furthermore, it is shown that the model has a unique classical global solution in two and three space dimensions if the chemotactic coefficients X1 and X2 are small as compared to the diffusion coefficient d3 of the chemoattractant.展开更多
文摘This paper is concerned with the sustained periodic oscillation phenomenon in a threespecies delayed predation system with Holling type II functional response and age structure in top predator.The top predator fertility function is regarded as a piecewise continuous smooth function with regard to their maturation period T2.The complicated dynamic behavior is proved by integrated semigroup theory and Hopf bifurcation theorem for semilinear equations with non-dense domain.Through qualitative analysis and bifurcation study of the system,we yield that this system has a nontrivial periodic solution that bifurcates from the positive equilibrium age distribution when bifurcation parameter T passes through some critical values.Numerical simulations are also provided to illustrate theoretically analytical results.
基金supported by NSF of China(11861056)NSF of Gansu Province(21JR7RA121)+1 种基金Department of Education of Gansu Province:Youth Doctoral Fund Project(2021QB-018)Northwest Normal University:Starting Fund for Doctoral Research(202103101204)。
文摘In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.
基金supported by NSF of China (11861056)NSF of Gansu Province (21JR7RA121)Department of Education of Gansu Province:Youth Doctoral Fund Project (2021QB-018).
文摘This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.
基金The second author is supported by NSF of China(11861056).
文摘In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Then,by constructing suitable upper solu-tions,we give some general conditions to ensure the linear determinacy of the minimalspeed.Finally,we provide some more precise conditions that only rely on the parametersof the system such that the linear determinacy of the minimal speed is assured.
基金This work is supported by the National Natural Science Foundation of China （Nos. 11361055, 11761063 and 11661051）, the Natural Science Foundation of Gansu Province （No. 1606RJZA038）, the National Statistical Scientific Research Projects （No. 2017LZ41）, and the Scientific Study Project for Gansu Province Institutes of Higher Learning （No. 2017B-41）.
文摘In this paper, we investigate the global existence of nonnegative solutions of a two- species Keller-Segel model with Lotka-Volterra competitive source terms. By raising the regularity of a solution from L^1 to L^p（p〉1）, the existence and uniqueness of the classical global in time solution to this chemotaxis model is proved for any chemotactic coefficients X1, X2 〉 0 when the space dimension is one. Furthermore, it is shown that the model has a unique classical global solution in two and three space dimensions if the chemotactic coefficients X1 and X2 are small as compared to the diffusion coefficient d3 of the chemoattractant.
