In the 1960’s Brian Goodwin published a couple of mathematical models showing how feedback inhibition can lead to oscillations and discussed possible implications of this behaviour for the physiology of the cell. He also presented key ideas about the rich dynamics that may result from the coupling between such biochemical oscillators. Goodwin’s work motivated a series of theoretical investigations aiming at identifying minimal mechanisms to generate limit cycle oscillations and deciphering design principles of biological oscillators. The three-variable Goodwin model (adapted by Griffith) can be seen as a core model for a large class of biological systems, ranging from ultradian to circadian clocks. We summarize here main ideas and results brought by Goodwin and review a couple of modeling works directly or indirectly inspired by Goodwin’s findings.

中文翻译：

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古德温振荡器及其遗产

在 1960 年代，Brian Goodwin 发表了几个数学模型，展示了反馈抑制如何导致振荡，并讨论了这种行为对细胞生理学的可能影响。他还提出了有关可能由此类生化振荡器之间的耦合产生的丰富动力学的关键思想。Goodwin 的工作激发了一系列理论研究，旨在确定产生极限循环振荡的最小机制并破译生物振荡器的设计原理。三变量古德温模型（由格里菲斯改编）可以被看作是一大类生物系统的核心模型，范围从超昼到生物钟。我们在这里总结了 Goodwin 带来的主要思想和结果，并回顾了一些直接或间接受 Goodwin 发现启发的建模工作。