Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on network cycles which support global Hopf bifurcation, i.e. global bifurcation of non-stationary time-periodic solutions from stationary solutions. Specifically, we show how monotone feedback cycles of the linearization at stationary solutions give rise to global Hopf bifurcation, for sufficiently dominant coefficients along the cycle.We include four example networks which feature such strong feedback cycles of length three and larger: Oregonator chemical reaction networks, Lotka-Volterra ecological population dynamics, citric acid cycles, and a circadian gene regulatory network in mammals. Reaction kinetics in our approach are not limited to mass action or Michaelis-Menten type.

中文翻译：

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具有快速反馈周期的网络中的全球Hopf分叉

自主的持续振荡在有生命和无生命系统中无处不在。作为开放系统，远离热力学平衡，它们无视熵定律，熵定律要求收敛到平稳。我们给出了支持全局Hopf分支的网络周期的结构条件，即固定时间解的非平稳时间周期解的全局分支。具体来说，我们展示了固定解线性化的单调反馈循环如何导致全局Hopf分叉，以及沿循环具有足够优势的系数。我们包括四个示例网络，这些网络具有如此长的长度为3或更大的强反馈循环：俄勒冈化学反应网络，Lotka-Volterra生态种群动态，柠檬酸循环和哺乳动物的昼夜节律基因调控网络。