By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficien...By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.展开更多
By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f...By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.展开更多
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soli...Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.展开更多
FDG-PET is of clinical value especially for detection of distant metastases or recurrent esophageal cancer. For the staging of primary tumor or locoregional lymph node metastasis PET is cur- rently not suitable.
The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and g...The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.展开更多
The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the ...The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.展开更多
The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is ...The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.展开更多
基金Supported by the Science Foundation of Hangzhou Dianzi University(KYF091504021)Supported by the Science Foundation of China Jiliang University(XZ0442)
文摘By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.
基金Supported by the National Natural Sciences Foundation of China(10361006)Supported by the Natural Sciences Foundation of Yunnan Province(2003A0001M)Supported by the Jiangsu "Qing-lanProject" for Excellent Young Teachers in University(2006)
文摘By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form {△x（n）=-b（n）x（n）＋f（n,x（n-τ1（n））,…,x（n-τm（n））,u（n-δ（n）））,△u（n）=-η（n）u（n）＋a（n）x（n-σ（n））,n∈Z.
文摘Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.
文摘FDG-PET is of clinical value especially for detection of distant metastases or recurrent esophageal cancer. For the staging of primary tumor or locoregional lymph node metastasis PET is cur- rently not suitable.
文摘The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of posi- tive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.
文摘The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.
文摘The purpose of this work is to study the spatial dynamics of a periodic reaction-diffusion epidemic model arising from the spread of oral-faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.
