By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]...By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].展开更多
During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing.The number density of ...During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing.The number density of active domains ρ decreases as the height h increases.A simple scaling argument leads to a scaling law of ρ~ h^（-γ） with a coarsening exponent γ=d/z,where d is the dimension of the substrate surface and z the dynamic exponent of a growth front.This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional（d=2） surface,even when an isolated deposited particle diffuses on a crystal surface.展开更多
An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill...An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution,展开更多
文摘By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].
文摘During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing.The number density of active domains ρ decreases as the height h increases.A simple scaling argument leads to a scaling law of ρ~ h^（-γ） with a coarsening exponent γ=d/z,where d is the dimension of the substrate surface and z the dynamic exponent of a growth front.This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional（d=2） surface,even when an isolated deposited particle diffuses on a crystal surface.
基金Supported by the National Natural Science Foundation of China (10171056).
文摘An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution,
