Before revision: Effects of the period mismatch on entrainment properties in two coupled genetic oscillators are studied. The entrainment is calculated with a phase reduction approach and a Floquet multiplier analysis, and their dependencies on coupling strength and the period ratio are investigated in two genetic oscillator models (smooth and relaxation oscillators).
After revision: Biological oscillators coordinate individual cellular components to function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch between them is unavoidable in biological implementations. We investigated the advantageous effect of the period mismatch in terms of synchronization against external stimuli (or trainability). Specifically, we numerically analyzed two fundamental genetic models, smooth and relaxation oscillators, on their trainability for different coupling strength and the period ratio are investigated in two genetic oscillator models (smooth and relaxation oscillators).