非线性Klein-Gordon三聚体中的局域能量脉动：极限相轨迹的高维类似物
Regimes of local energy pulsations in non-linear Klein-Gordon trimer: Higher dimensional analogs of limiting phase trajectories
摘要：
在本文中，我们考虑的动力学的特殊类调制制度出现在克莱因-戈登三聚体。特别是，这项研究揭示了独特的状态，共振能量转移所表现出的规则的能量脉动本地化的前两个元素的链。这种状态被认为是在2DOF，非谐，振荡模型中的最大能量转移的政权对应的限制相轨迹的高维模拟。我们表明，在限制相轨迹相反，这种特殊的状态出现在克莱因-戈登三聚体的局部能量转移经历额外的过渡，导致其完全消除。通过采用特殊的降阶过程，我们解析地描述了这种特殊的动力学状态的形成和破坏的机制。最后，我们证明了这种状态的分叉之间的强相关性的一系列自发过渡从本地化到离域的能量脉动所经历的脉冲响应的克莱因-戈登三聚体。分析模型的结果与数值模拟结果吻合较好。
英文摘要：
In the present paper we consider the dynamics of special class of modulated regimes emerging in the Klein-Gordon trimer. In particular, this study unveils the unique states of resonant energy transfer manifested by the regular energy pulsations localized on the first two elements of the chain. This state is regarded as the higher dimensional analog of limiting phase trajectory corresponding to the regime of maximal energy transfer in the 2DOF, anharmonic, oscillatory models. We show that in contrast to the limiting phase trajectories, this special state of local energy transfer emerging in the Klein-Gordon trimer undergoes additional transition leading to its complete elimination. By employing the special order reduction procedure, we describe analytically the mechanism of formation and destruction of this peculiar, dynamical state. Finally, we demonstrate the strong correlation between the bifurcations of this state to the series of spontaneous transitions from localized to delocalized energy pulsations undergone by the impulsive response of the Klein-Gordon trimer. Results of the analytical model are well in agreement with these of the numerical simulations.
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