We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding t...We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.展开更多
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
基金supported by National Natural Science Foundation of China (Grant Nos.11171051 and 91230103)
文摘We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.
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.
