With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical conditio...With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.展开更多
In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model...In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.展开更多
The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques o...The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator’s net uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).展开更多
文摘With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.
基金Supported by the National Natural Science Foundation of China (No.10171106)
文摘In most models of population dynamics, diffusion between patches is assumedto be continuous or discrete, but in practice many species diffuse only during a single period. Inthis paper we propose a single species model with impulsive diffusion between two patches, whichprovides a more natural description of population dynamics. By using the discrete dynamical systemgenerated by a monotone, concave map for the population, we prove that the map always has a globallystable positive fixed point. This means that a single species system with impulsive diffusionalways has a globally stable positive periodic solution. This result is further substantiated bynumerical simulation. Under impulsive diffusion the single species survives in the two patches.
基金supported by National Natural Science Foundation of China 10171106
文摘The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator’s net uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).
