In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternativ...In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B...A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.展开更多
This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate...This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.展开更多
In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic so...In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).展开更多
By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x ...By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.展开更多
The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of syste...The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.展开更多
We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function of a character of species whose evolution obeys a quantitative genetic model. We will show th...We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function of a character of species whose evolution obeys a quantitative genetic model. We will show that the structure of a solution is rather different from that of a non-evolutional system. We will analytically show new ecological features of the dynamics.展开更多
文摘In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
基金Supported by the National Natural Science Foundation of China (10961017)"Qinglan" Talent Programof Lanzhou Jiaotong University (QL-05-20A)
文摘A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.
基金supported partly by the NSF (10971124,11001160) of ChinaNSC (972628-M-110-003-MY3) (Taiwan)the Fundamental Research Funds (GK201002046) for the Central Universities
文摘This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.
文摘In this paper a class of cooperative Lotka-Volterra population system with time delay is considered. Some sufficient conditions on the existence and globally asymptotically stability for the asymptotically periodic solution of the system are established by using the Lyapunov function method and the method given in Fengying Wei and Wang Ke (Applied Mathematics and Computation 182 (2006) 161-165).
文摘By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.
文摘The main purpose of this article is considering the persistence non-autonomous Lotka-Volterra system with predator-prey ratio-dependence and density dependence. We get the sufficient conditions of persistence of system, further have the necessary conditions, also the uniform persistence condition, which can be easily checked for the model is obtained.
文摘We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function of a character of species whose evolution obeys a quantitative genetic model. We will show that the structure of a solution is rather different from that of a non-evolutional system. We will analytically show new ecological features of the dynamics.
