Oscillation arrest in the mouse somitogenesis clock presumably takes   place via an infinite period bifurcation
  In this work we address the question of how oscillations are arrested in the mouse somitogenesis clock when the determination front reaches presomitic cells. Based upon available experimental evidence we hypothesize that the mechanism underlying such a phenomenon involves the interaction between a limit cycle (originated by a delayed negative feedback loop) and a bistable switch (originated by a positive feedback loop). With this hypothesis in mind we construct the simplest possible model comprising both negative and positive feedback loops and show that (with a suitable choice of paremeters): 1) it can show an oscillatory behavior, 2) oscillations are arrested via an infinite-period bifurcation whenever the different gene-expression regulator-inputs act together in an additive rather than in a multiplicative fashion, and 3) this mechanism for oscillation arrest is compatible whit plentiful experimental observations. 
Eder Zavala-L\'opez, Mois\'es Santill\'an
q-bio.CB physics.bio-ph