We consider a pair of coupled heterogeneous phase oscillator networks and investigate their dynamics in the continuum limit as the intrinsic frequencies of the oscillators are made more and more disparate. The Ott/Antonsen Ansatz is used to reduce the system to three ordinary differential equations. We find that most of the interesting dynamics, such as chaotic behaviour, can be understood by analysing a gluing bifurcation of periodic orbits; these orbits can be thought of as "breathing chimeras" in the limit of identical oscillators. We also add Gaussian white noise to the oscillators' dynamics and derive a pair of coupled Fokker-Planck equations describing the dynamics in this case. Comparison with simulations of finite networks of oscillators is used to confirm many of the results.
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机译：我们考虑一对耦合的异质相位振荡器网络，并随着振荡器的固有频率越来越不同而研究它们在连续极限内的动态。 Ott / Antonsen Ansatz用于将系统简化为三个常微分方程。我们发现，通过分析周期性轨道的胶合分叉，可以理解大多数有趣的动力学，例如混沌行为。在相同的振荡器范围内，这些轨道可以被认为是“呼吸嵌合体”。我们还将高斯白噪声添加到振荡器的动力学中，并得出一对耦合的Fokker-Planck方程，用于描述这种情况下的动力学。与振荡器有限网络的仿真比较可用于确认许多结果。
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