In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability,and show that there are not any periodic solutions in some a neibou...In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability,and show that there are not any periodic solutions in some a neibourhood of the equilibrium points of the dynamical systems.展开更多
In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability, and show that there are not any periodic solutions in some a neibo...In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability, and show that there are not any periodic solutions in some a neibourhed of the equilibrium points of the dynamical systems.展开更多
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relat...Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.展开更多
文摘In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability,and show that there are not any periodic solutions in some a neibourhood of the equilibrium points of the dynamical systems.
文摘In this paper, we consider the dynamical systems which are from a kind of Hamilton systems under a disturbance. We use theories in Liapunov stability, and show that there are not any periodic solutions in some a neibourhed of the equilibrium points of the dynamical systems.
基金Supported by the Special Fund of the National Fundamental Research (No. 2004CB217904)National Natural Science Foundation of China (No. 50595413)Program for New Century Excellent Talents in Universities, Fok Ying Tung Education Foundation (No.104019 )Foundation for the Authors of National Excellent Doctoral Dissertation (No. 200439) ,Key Project of Chinese Ministry of Education (No. 10047).
文摘Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.
