Ruan Dixian, Liu Junjie, Wu Changqin
Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China.
Department of Physics, International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China.
Phys Rev E. 2023 Aug;108(2-1):024207. doi: 10.1103/PhysRevE.108.024207.
The phenomenon of synchronization in self-sustained systems has been successfully illuminated in many fields, ranging from biology to electrical engineering. To date, the majority of theoretical studies on synchronization focus on isolated self-sustained systems, leaving the effects of surrounding environments less touched due to the lack of appropriate descriptions. Here we derive a generalized Langevin equation that governs the dynamics of open classical Van der Pol (VdP) oscillators immersed in a common thermal bath with arbitrary memory time and subsumes an existing equation for memoryless bath as a special limit. The so-obtained Langevin equation reveals that the bath can induce a dissipative coupling between VdP oscillators, besides the usual damping and thermal noise terms connected by the fluctuation-dissipation theorem. To demonstrate the utility of the approach, we investigate a model system consisting of two open VdP oscillators coupled to a thermal bath with an Ohmic or a Lorentzian-shape spectrum. Unlike the isolated setup where the stable synchronization can be either in-phase or antiphase when varying initial conditions, we find that the bath always favors a single type of synchronization in the long-time limit regardless of initial conditions and the synchronization type can be switched by tuning the temperature. Moreover, we show that the bath-induced dissipative coupling can trigger a synchronization of open VdP oscillators that is otherwise absent between isolated counterparts. Our results complement and extend previous findings for open VdP oscillators.
自维持系统中的同步现象已在从生物学到电气工程等众多领域得到成功阐释。迄今为止，大多数关于同步的理论研究都集中在孤立的自维持系统上，由于缺乏恰当描述，周围环境的影响较少涉及。在此，我们推导出一个广义朗之万方程，它描述了浸没在具有任意记忆时间的公共热浴中的开放经典范德波尔（VdP）振子的动力学，并且将一个用于无记忆热浴的现有方程作为特殊极限包含在内。如此得到的朗之万方程表明，除了由涨落耗散定理联系起来的通常的阻尼和热噪声项外，热浴还能在VdP振子之间诱导出一种耗散耦合。为了证明该方法的实用性，我们研究了一个由两个与具有欧姆或洛伦兹型谱的热浴耦合的开放VdP振子组成的模型系统。与孤立系统不同，在孤立系统中改变初始条件时稳定同步可以是同相或反相，我们发现热浴在长时间极限下总是倾向于单一类型的同步，而与初始条件无关，并且同步类型可以通过调节温度来切换。此外，我们表明热浴诱导的耗散耦合可以触发开放VdP振子的同步，而在孤立的振子之间原本不存在这种同步。我们的结果补充并扩展了先前关于开放VdP振子的研究发现。
