两个动能耦合Morse振子系统的分岔现象(英文)

Bifurcation Phenomena of Two Kinetically Coupled Morse Oscillators

从两个未耦合的Morse振子出发,首先研究了两个动能耦合的Morse振子系统局域模区域内的分岔结构.发现对弱耦合参数δ,相空间中局域模谐振mn共存与系统能量ε通过不等式2^(1/1-ε)≥m/n≥2^(1-ε)相关联.同时报导了对称伸缩本征模的分岔现象与能量及耦合常数的关系.在弱耦合参数δ下,在非常低的能量区域内,对称伸缩经历一个pitch-fork分岔.随后,局域模随能量的增加逐渐形成.对中等高能量ε,对称伸缩本征征模在耦合参数范围[-1,0]内由不稳定到稳定到不稳定等交替变化.

Starting from two uncoupled Morse oscillators, this paper first studied the bifurcation structures in the local mode region in phase space for two kinetically coupled Morse oscillators. It turns out that local mode resonances n/m coexistence in phase space for a weak coupling parameter δ relating to the system energy ε through the inequality equation √1/1-ε≥n/m≥√1-εThis paper also reports the bifurcation phenomena of symmetric stretch normal mode with both system energy ε and coupling parameter . At a weak coupling parameter δ,the symmetric stretch experiences a pitch fork bifurcation at a very low energy domain, then the local mode regions are gradually formed with system energy. For an intermediate high energy ε, the symmetric stretch normal mode stays stable and unstable alternatively with coupling parameter 6 in the range [ - 1,0 ].