This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability o...This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].展开更多
This note is devoted to the son＇s blowflies equation with diffusion, a critical speed of traveling waves, we give behavior with respect to the mature age study on the traveling wavefronts to the Nicholtime-delayed re...This note is devoted to the son＇s blowflies equation with diffusion, a critical speed of traveling waves, we give behavior with respect to the mature age study on the traveling wavefronts to the Nicholtime-delayed reaction-diffusion equation. For the a detailed analysis on its location and asymptotic展开更多
In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for...In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.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
A new method is presented to display ultrasonic traveling wavefront by colltinuously modulated laser diode based on the temporal correlation theory. It is proved by experimeot.
In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations...In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma（J Differential Equations,2001,171：294-314. ）.展开更多
This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R...This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.展开更多
This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with l...This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with lower and upper bound.Especially,state-dependent delay is introduced into a nonlocal reaction-diffusion model.The conditions of Schauder's fixed point theorem are proved by constructing a reasonable set of functionsΓ(see Section 2)and a pair of upper-lower solutions,so the existence of traveling wavefronts is established.The present study is continuation of a previous work that highlights the Laplacian diffusion.展开更多
基金supported by NSF of China(11401478)Gansu Provincial Natural Science Foundation(145RJZA220)
文摘This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts （waves with speeds c 〉 c＊, where c=c＊ is the minimal speed） is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x → -∞, but it can be allowed arbitrary large in other locations, which improves the results in[9, 18, 21].
基金supported by Natural Sciences and Engineering Research Council of Canada under the NSERC grant RGPIN 354724-08
文摘This note is devoted to the son＇s blowflies equation with diffusion, a critical speed of traveling waves, we give behavior with respect to the mature age study on the traveling wavefronts to the Nicholtime-delayed reaction-diffusion equation. For the a detailed analysis on its location and asymptotic
基金partially supported by the National Natural Science Foundation of China(11671359)the Provincial Natural Science Foundation of Zhejiang(LY15A010017,LY16A010009)the Science Foundation of Zhejiang Sci-Tech University 15062173-Y
文摘In this paper, we study the propagation of the pattern for a reaction-diffusionchemotaxis model. By using a weakly nonlinear analysis with multiple temporal and spatial scales, we establish the amplitude equations for the patterns, which show that a local perturbation at the constant steady state is spread over the whole domain in the form of a traveling wavefront. The simulations demonstrate that the amplitude equations capture the evolution of the exact patterns obtained by numerically solving the considered system.
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.
文摘A new method is presented to display ultrasonic traveling wavefront by colltinuously modulated laser diode based on the temporal correlation theory. It is proved by experimeot.
文摘In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma（J Differential Equations,2001,171：294-314. ）.
基金Project supported by the National Natural Science Foundation of China (No. 10961017)the"Qing Lan" Talent Engineering Funds of Lanzhou Jiaotong University (No. QL-05-20A)
文摘This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.
基金Supported by NSFC(Grant Nos.11771044,11871007)Foundation of Anhui University of Finance and Economics(Grant No.ACKYC19051)Major Research Projects of Natural Science in Colleges and Universities of Anhui Province(Grant No.KJ2017ZD35)
文摘This paper is concerned with the travelling wavefronts of a nonlocal dispersal cooperation model with harvesting and state-dependent delay,which is assumed to be an increasing function of the population density with lower and upper bound.Especially,state-dependent delay is introduced into a nonlocal reaction-diffusion model.The conditions of Schauder's fixed point theorem are proved by constructing a reasonable set of functionsΓ(see Section 2)and a pair of upper-lower solutions,so the existence of traveling wavefronts is established.The present study is continuation of a previous work that highlights the Laplacian diffusion.
