标题： 时间延迟耦合对网络振荡集体频率的影响 显示英文标题

标题： Effects of time-delay couplings in the collective frequency of network oscillations

摘要： 在本研究中，我们构建了这样的系统，使用全局耦合振荡器的Kuramoto模型，具有时间延迟的正耦合和负耦合，以探索耦合时间延迟对同步振荡集体频率的影响。 我们讨论了各种相同和不同系统的固定和指数分布延迟，并推导了稳定同步状态下耦合延迟与集体频率之间的关系。 对于耦合振荡器的不同系统，我们考虑了固有频率的洛伦兹分布和耦合时间延迟的指数分布，并解析地推导了集体频率与时间延迟之间的关系。 我们发现网络振荡的集体频率取决于耦合强度和时间延迟。 在相同的情况下，大多数正耦合情况下网络频率降低，而在负耦合情况下随着增加而增加。 在具有分布延迟的不同情况下，除了网络频率的调制外，我们还讨论了时间延迟耦合可能导致系统行为中分岔和转变的出现，从而导致新模式的产生和现有模式的破坏。 我们讨论了这些结果在理解自然系统行为中的意义。 显示英文摘要

摘要： In this study, we construct such systems with the Kuramoto model of globally coupled oscillators with time-delayed positive and negative couplings to explore the impact of coupling time delays in the collective frequency of synchronized oscillations. We discuss various identical and nonidentical systems with fixed and exponential distributed delays and derive relationships between the coupling delay and collective frequency for a stably synchronized state. For the nonidentical system of coupled oscillators, we consider the Lorentzian distribution of intrinsic frequencies and exponential distributions of coupling time delays in coupled oscillators, and analytically derived the collective frequency-time delay relationship. We found that the collective frequency of the network oscillations is dependent on both coupling strength and time delay. In identical cases, the network frequency decreases in most cases of positive coupling and increases in a negative coupling with increasing. In non-identical cases with distributed delays, along with the modulations in the network frequency, we discussed time-delay coupling can also lead to the appearance of bifurcations and transitions in the system's behavior resulting in the emergence of new patterns and the breakdown of existing ones. We discuss the implications of these results in understanding the behaviors of the natural systems.