Cartwright Julyan H E, Magnasco Marcelo O, Piro Oreste, Tuval Idan
Laboratorio de Estudios Cristalográficos, CSIC, E-18071 Granada, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016217. doi: 10.1103/PhysRevE.68.016217. Epub 2003 Jul 21.
We establish and investigate the conceptual connection between the dynamics of the bailout embedding of a Hamiltonian system and the dynamical regimes associated with the occurrence of bubbling and blowout bifurcations. The roles of the invariant manifold and the dynamics restricted to it, required in bubbling and blowout bifurcating systems, are played in the bailout embedding by the embedded Hamiltonian dynamical system. The Hamiltonian nature of the dynamics is precisely the distinctive feature of this instance of a bubbling or blowout bifurcation. The detachment of the embedding trajectories from the original ones can thus be thought of as transient on-off intermittency, and noise-induced avoidance of some regions of the embedded phase space can be recognized as Hamiltonian bubbling.
我们建立并研究了哈密顿系统的救助嵌入动力学与与气泡和爆裂分岔发生相关的动力学机制之间的概念联系。在气泡和爆裂分岔系统中所需的不变流形及其上受限动力学的作用，在救助嵌入中由嵌入的哈密顿动力系统来扮演。动力学的哈密顿性质正是这种气泡或爆裂分岔情况的独特特征。因此，嵌入轨迹与原始轨迹的分离可以被视为瞬态通断间歇性，并且噪声诱导的对嵌入相空间某些区域的回避可以被识别为哈密顿气泡。
