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
Zr-4(Zr-1.5Sn-0.2Fe-0.1Cr,wt%), S5(Zr-0.8Sn-0.34Nb-0.39Fe-0.1Cr), T5(Zr-0.7Sn-1.07Nb-0.32Fe-0.08Cr) and Zr-1Nb were adopted to prepare Bi-containing zirconium alloys for systematically investigating the effect of Bi a...Zr-4(Zr-1.5Sn-0.2Fe-0.1Cr,wt%), S5(Zr-0.8Sn-0.34Nb-0.39Fe-0.1Cr), T5(Zr-0.7Sn-1.07Nb-0.32Fe-0.08Cr) and Zr-1Nb were adopted to prepare Bi-containing zirconium alloys for systematically investigating the effect of Bi addition on the corrosion resistance of zirconium alloys. The specimens were corroded in superheated steam at 400℃/10.3 MPa, and in lithiated water with 0.01 M LiOH or in deionized water at 360℃/18.6 MPa by autoclave testing. Results show that the corrosion resistance increases with the increasing of Bi content dissolved in α-Zr. But the presence of Bi-con- taining second phase particles (SPPs) is unfavorable for the enhancement of corrosion resistance. This indicates that the Bi dissolved in α-Zr matrix plays an important role in improving the corrosion resistance, while the precipitation of the Bi-containing SPPs does harm to the corrosion resistance.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. .
文摘Zr-4(Zr-1.5Sn-0.2Fe-0.1Cr,wt%), S5(Zr-0.8Sn-0.34Nb-0.39Fe-0.1Cr), T5(Zr-0.7Sn-1.07Nb-0.32Fe-0.08Cr) and Zr-1Nb were adopted to prepare Bi-containing zirconium alloys for systematically investigating the effect of Bi addition on the corrosion resistance of zirconium alloys. The specimens were corroded in superheated steam at 400℃/10.3 MPa, and in lithiated water with 0.01 M LiOH or in deionized water at 360℃/18.6 MPa by autoclave testing. Results show that the corrosion resistance increases with the increasing of Bi content dissolved in α-Zr. But the presence of Bi-con- taining second phase particles (SPPs) is unfavorable for the enhancement of corrosion resistance. This indicates that the Bi dissolved in α-Zr matrix plays an important role in improving the corrosion resistance, while the precipitation of the Bi-containing SPPs does harm to the corrosion resistance.
