In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochast...In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .展开更多
The magnetic cooling utilizing magneto-caloric effect is recognized as promising energy efficiency and environmentally friendly technology.Here we report a systematical study on the microstructures,magnetic properties...The magnetic cooling utilizing magneto-caloric effect is recognized as promising energy efficiency and environmentally friendly technology.Here we report a systematical study on the microstructures,magnetic properties and cryogenic magneto-caloric performances of the Gd_(20)Ho_(20)Tm_(20)Cu_(20)Ni_(20) amorphous ribbons.It is found that the ribbons reveal a second-order phase transition and are accompanied by a table-shaped magneto-caloric effect.The calculated magneticentropy-change maximum |ΔSM|,temperature averaged entropy change(i.e.,TEC(10)),and refrigerant capacity reach 13.9 J/kg·K,13.84 J/kg-K and 740 J/kg with magnetic field change of 0-7 T,respectively,indicating that the present Gd_(20)Ho_(20)Tm_(20)Cu_(20)Ni_(20) amorphous ribbons are good candidates for magnetic cooling.展开更多
文摘In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .
基金Project supported by the National Natural Science Foundation of China(Grant No.52071197)the Science and Technology Committee of Shanghai(Grant No.19ZR1418300)+2 种基金the Independent Research and Development Project of State Key Laboratory of Advanced Special SteelShanghai Key Laboratory of Advanced Ferrometallurgy,Shanghai University(Grant No.SKLASS 2019-Z003)the Science and Technology Commission of Shanghai Municipality(Grant No.19DZ2270200)。
文摘The magnetic cooling utilizing magneto-caloric effect is recognized as promising energy efficiency and environmentally friendly technology.Here we report a systematical study on the microstructures,magnetic properties and cryogenic magneto-caloric performances of the Gd_(20)Ho_(20)Tm_(20)Cu_(20)Ni_(20) amorphous ribbons.It is found that the ribbons reveal a second-order phase transition and are accompanied by a table-shaped magneto-caloric effect.The calculated magneticentropy-change maximum |ΔSM|,temperature averaged entropy change(i.e.,TEC(10)),and refrigerant capacity reach 13.9 J/kg·K,13.84 J/kg-K and 740 J/kg with magnetic field change of 0-7 T,respectively,indicating that the present Gd_(20)Ho_(20)Tm_(20)Cu_(20)Ni_(20) amorphous ribbons are good candidates for magnetic cooling.
