论文标题
关于非$ {\ cal {pt}} $的常规和混乱动力学 - 对称耦合的振荡振荡器的对称hamiltonian系统，具有平衡的损失和增益
On regular and chaotic dynamics of a non-${\cal{PT}}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
论文作者
论文摘要
一个非对称的振荡器的对称的哈密顿系统，该系统偶联到具有可变的角频率的抗抑制振荡器的对称的振荡器的对称的hamiltonian系统，以允许定期解决方案。结果意味着$ {\ cal {pt}} $ - 对具有平衡损失和增益的哈密顿系统的对称性是为了接纳定期解决方案。哈密顿量描述了一个多稳态的动力系统 - 五个平衡点中的三个是稳定的。通过使用扰动和数值方法详细研究了模型的动力学，并证明可以在参数空间的某些区域接受周期性解决方案。从周期性到无界解决方案的相变，必须了解$ {\ cal {pt}} $ - symmetry，而无需任何引用。数值分析揭示了系统中混乱的行为，超出了参数的临界值，该参数将振荡器耦合到抗抑制的谐波振荡器，从而为系统中的汉密尔顿混乱的第一个例子与平衡的损失和增益提供了第一个例子。多个时间尺度的方法用于扰动研究系统。在扰动的领先顺序上，振幅的动力学由具有平衡损耗和增益的有效二聚体模型控制，而不是 - $ {\ cal {pt}} $ - 对称的汉密尔顿系统。二聚体模型是通过使用Stokes变量准确求解的，并显示出在参数空间的某些区域的周期性解决方案。
A non-${\cal{PT}}$-symmetric Hamiltonian system of a Duffing oscillator coupled to an anti-damped oscillator with a variable angular frequency is shown to admit periodic solutions. The result implies that ${\cal{PT}}$-symmetry of a Hamiltonian system with balanced loss and gain is not necessary in order to admit periodic solutions. The Hamiltonian describes a multistable dynamical system - three out of five equilibrium points are stable. The dynamics of the model is investigated in detail by using perturbative as well as numerical methods and shown to admit periodic solutions in some regions in the space of parameters. The phase transition from periodic to unbounded solution is to be understood without any reference to ${\cal{PT}}$-symmetry. The numerical analysis reveals chaotic behaviour in the system beyond a critical value of the parameter that couples the Duffing oscillator to the anti-damped harmonic oscillator, thereby providing the first example of Hamiltonian chaos in a system with balanced loss and gain. The method of multiple time-scales is used for investigating the system perturbatively. The dynamics of the amplitude in the leading order of the perturbation is governed by an effective dimer model with balanced loss and gain that is non-${\cal{PT}}$-symmetric Hamiltonian system. The dimer model is solved exactly by using the Stokes variables and shown to admit periodic solutions in some regions of the parameter space.
