By introducing periodic switching signal associated with illumination to the Originator,a switched mathematical model has been established.The bifurcation sets are derived based on the characteristics of the equilibri...By introducing periodic switching signal associated with illumination to the Originator,a switched mathematical model has been established.The bifurcation sets are derived based on the characteristics of the equilibrium points.Two types of periodic oscillation,such as 2T-focus/cycle periodic switching and 2T-focus/focus periodic switching,have been observed,the mechanism of which is presented through the switching relationship.The distribution of eigenvalues related to the equilibrium points determined by two subsystems is discussed to interpret oscillation-increasing and oscillation-decreasing cascades of the periodic oscillations.Furthermore,the invariant subspaces of the equilibrium point are investigated to reveal the mechanism of dynamical phenomena in the periodic switching.展开更多
A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclin...A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of the bifurcation equation, the authors obtain the conditions when the original flip homoclinic orbit is kept or broken. The existence and the existence regions of several double periodic orbits and one triple periodic orbit bifurcations are proved. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 20976075 and 10972091)College Graduate Student Scientific Research Innovation Foundation of Jiangsu,China (Grant No. CXLX12-0619)
文摘By introducing periodic switching signal associated with illumination to the Originator,a switched mathematical model has been established.The bifurcation sets are derived based on the characteristics of the equilibrium points.Two types of periodic oscillation,such as 2T-focus/cycle periodic switching and 2T-focus/focus periodic switching,have been observed,the mechanism of which is presented through the switching relationship.The distribution of eigenvalues related to the equilibrium points determined by two subsystems is discussed to interpret oscillation-increasing and oscillation-decreasing cascades of the periodic oscillations.Furthermore,the invariant subspaces of the equilibrium point are investigated to reveal the mechanism of dynamical phenomena in the periodic switching.
基金supported by the National Natural Science Foundation of China(No.11126097)
文摘A high-codimension homoclinic bifurcation is considered with one orbit flip and two inclination flips accompanied by resonant principal eigenvalues. A local active coordinate system in a small neighborhood of homoclinic orbit is introduced. By analysis of the bifurcation equation, the authors obtain the conditions when the original flip homoclinic orbit is kept or broken. The existence and the existence regions of several double periodic orbits and one triple periodic orbit bifurcations are proved. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately.
