Coalescence of limit cycles in the presence of noise
Coalescence of limit cycles in the presence of noise
复制标题
存在噪声时极限环的合并
DOI：
10.1103/physreve.109.024220
复制
发表时间：
2024
影响因子：
2.4
通讯作者：
Littlewood, Peter B.
中科院分区：
文献类型：
--
作者：
Shmakov, Sergei;Littlewood, Peter B.
复杂的动力系统可能会表现出多个稳态，包括时间周期极限环，其中最终的轨迹取决于初始条件。随着参数的调整，极限环可以增殖或合并在一个特殊的点。在这里，我们问如何在这样的分岔附近的动态噪声的影响。一个干草叉分叉可以用来诱导分叉行为。我们模型的极限环的正常形式的霍普夫振荡器，耦合到干草叉，并调查所产生的动力系统中存在的噪声。我们表明，生成功能的平均动力学变量之间的干草叉和振荡器的因式分解。干草叉的统计特性的存在下，在其各种制度的噪声进行了研究和相关性和响应函数，包括一个可能的破磁场的标度理论。分析是通过微扰计算以及数值手段。最后，观察说明耦合的系统与极限环的干草叉进行了讨论和相位相位的相关性表现出非扩散行为与普遍的标度。
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional point. Here we ask how dynamics in the vicinity of such a bifurcation are influenced by noise. A pitchfork bifurcation can be used to induce bifurcation behavior. We model a limit cycle with the normal form of the Hopf oscillator, couple it to the pitchfork, and investigate the resulting dynamical system in the presence of noise. We show that the generating functional for the averages of the dynamical variables factorizes between the pitchfork and the oscillator. The statistical properties of the pitchfork in the presence of noise in its various regimes are investigated and a scaling theory is developed for the correlation and response functions, including a possible symmetry-breaking field. The analysis is done by perturbative calculations as well as numerical means. Finally, observables illustrating the coupling of a system with a limit cycle to a pitchfork are discussed and the phase-phase correlations are shown to exhibit nondiffusive behavior with universal scaling.