Dynamics of the Tyson–Hong–Thron–Novak circadian oscillator model

We study the dynamics of a circadian oscillator model proposed by Tyson, Hong, Thron and Novak. This describes molecular mechanism for rhythm in Drosophila. After giving detailed its equilibria, we investigate cases that rate mRNA degradation is sufficiently high or low. When high, prove there are no periodic orbits region with biological meaning. low, this transformed into slow–fast system. Then based on geometric singular perturbation theory, existence relaxation oscillations, canard explosion, saddle–node bifurcations, coexistence two limit cycles model. These results helpful to understand effects biophysical parameters oscillations. Finally, give interpretation point out can be Liénard-like equation, which could general case. • Investigated Discovered when high. Studied complex Proved orbits.