Institute of Neuroinformatics and Institute of Computational Science, University of Zurich and ETH Zurich, 8057 Zurich, Switzerland.
Phys Rev Lett. 2016 Mar 11;116(10):108101. doi: 10.1103/PhysRevLett.116.108101. Epub 2016 Mar 9.
Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale invariance, from a general level, applicable to all dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., neuronal Hodgkin-Huxley equations). When subject to natural "signal coupling," ensembles of Hopf systems below the bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs at parameter values substantially below where the average of the individual systems would bifurcate, with a frequency profile that is sharpened if compared to the individual systems.
生物传感器的惊人特性通常可以映射到分岔发生以下的动力学系统上。对于哺乳动物的听觉，Hopf 分岔描述已被证明在整个范围内都有效，从单个毛束到耳蜗的整个区域。我们在这里揭示了这种标度不变性的起源，从一般水平上，适用于 Hopf 分岔附近的所有动力学（包括神经元 Hodgkin-Huxley 方程）。当受到自然“信号耦合”的影响时，分岔阈值以下的 Hopf 系统集合表现出集体 Hopf 分岔。这种集体 Hopf 分岔发生在参数值大大低于个体系统分岔的平均值的地方，如果与个体系统相比，其频率谱会更加尖锐。
