Abstract
Two identical van der Pol oscillators with mutual inhibition are considered as a conceptual framework for modeling a latching mechanism for cell cycle regulation. In particular, the oscillators are biased to a latched state in which there is a globally attracting steady-state equilibrium without coupling. The inhibitory coupling induces stable alternating large-amplitude oscillations that model the normal cell cycle. A homoclinic bifurcation within the model is found to be responsible for the transition from normal cell cycling to endocycles in which only one of the two oscillators undergoes large-amplitude oscillations.
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•A latching mechanism in the cell division cycle is captured by coupled oscillators•The two identical oscillators are excitable (i.e., latched in the cell cycle)•Alternating oscillations, induced by mutual inhibition, model the normal cell cycle•Endocycles are represented by asymmetric states with one large-amplitude oscillator•Normal cell cycling transitiions to endocycles through a homoclinic bifurcation