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Hopf bifurcation with zero frequency and imperfect SO(2) symmetry
Hopf bifurcation zero frequency imperfect SO(2) symmetry Dynamical Systems
2012/6/29
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dy...
Characterizing mixed mode oscillations shaped by noise and bifurcation structure
mixed mode oscillations underlying dynamical structure extrinsic noise
2010/4/2
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different...
Bifurcation of limit cycles from quintic Hamiltonian with a double figure eight loop
动力系统 Conley理论 持续性 周期解 Abel积分
2008/4/25
Hilbert 16 问题的重要意义已是众所周知,但迄今尚未解决。为此，Arnold于1977年提出了弱Hilbert 16 问题，但也未解决。本项目首先研究与该问题有关的课题，讨论了三次和n次扰动的单参数Hamilton系统，得到了Abel积分的零点个数的上界估计。对具不变直线的二次系统极限环的唯一性定理，我们给出了完整的证明。对以柱面为首次积分的空间三次系统，我们得到在每个柱面上至多有三个周期...
An SMIB model in the power systems, especially thatconcering the effects of hard limits on bifurcations, chaos andstability is studied. Parameter conditions for bifurcations andchaos in the absence of...