The stability question of large-scale horizontal motion in the atmosphere under the effect of Rossby parameter is discussed in this paper by using the qualitative analysis theory of ordinary differential equations. Th...The stability question of large-scale horizontal motion in the atmosphere under the effect of Rossby parameter is discussed in this paper by using the qualitative analysis theory of ordinary differential equations. The following aspects are reviewed: The stability of large-scale horizontal motion in the atmosphere accords with the common inertial stability criterion when the effect of Rossby parameter is not considered (Yang, 1983), and that, on the other hand, the motion will bifurcate two times with the variation of absolute vorticity of basic Zephyr flow at the initial position under the effect of Rossby parameter. Furthermore, in the inertial stable region, if the effect of geostrophic deviation at the initial position is considered, the motion will not only bifurcate but also generate a catastrophe.展开更多
Many realistic social networks share some universal characteristic properties,such as the small-world effects and the heterogeneous distribution of connectivity degree,which affect the dynamics in society system,espec...Many realistic social networks share some universal characteristic properties,such as the small-world effects and the heterogeneous distribution of connectivity degree,which affect the dynamics in society system,especially the opinion dynamics in society.To see this,we study the opinion dynamics of the Improved Deffuant Model(IDM)in complex networks.When the two opinions differ by less than the confidence parameterǫ(0<ǫ<1),each opinion moves partly in the direction of the other with the convergence parameterµ,which is a function of the opposite’s degree k;otherwise,the two refuse to discuss and no opinion is changed.We analyze the evolution of the steady opinion s∗as a function of the confidence parameterǫ,the relation between the minority steady opinion smin∗and the individual connectivity k,and find some interesting results that show the dependence of the opinion dynamics on the confidence parameter and on the system topology.This study provides a new perspective and tools to understand the effects of complex system topology on opinion dynamics.展开更多
文摘The stability question of large-scale horizontal motion in the atmosphere under the effect of Rossby parameter is discussed in this paper by using the qualitative analysis theory of ordinary differential equations. The following aspects are reviewed: The stability of large-scale horizontal motion in the atmosphere accords with the common inertial stability criterion when the effect of Rossby parameter is not considered (Yang, 1983), and that, on the other hand, the motion will bifurcate two times with the variation of absolute vorticity of basic Zephyr flow at the initial position under the effect of Rossby parameter. Furthermore, in the inertial stable region, if the effect of geostrophic deviation at the initial position is considered, the motion will not only bifurcate but also generate a catastrophe.
基金This work was supported by the National Natural Science Foundation of China under Grants 70571027,10635020by the Ministry of Education in China under Grant 306022.
文摘Many realistic social networks share some universal characteristic properties,such as the small-world effects and the heterogeneous distribution of connectivity degree,which affect the dynamics in society system,especially the opinion dynamics in society.To see this,we study the opinion dynamics of the Improved Deffuant Model(IDM)in complex networks.When the two opinions differ by less than the confidence parameterǫ(0<ǫ<1),each opinion moves partly in the direction of the other with the convergence parameterµ,which is a function of the opposite’s degree k;otherwise,the two refuse to discuss and no opinion is changed.We analyze the evolution of the steady opinion s∗as a function of the confidence parameterǫ,the relation between the minority steady opinion smin∗and the individual connectivity k,and find some interesting results that show the dependence of the opinion dynamics on the confidence parameter and on the system topology.This study provides a new perspective and tools to understand the effects of complex system topology on opinion dynamics.
