Van der Pol networks with symmetry

Concerns the modelling of biological control with rhythm, especially the mammalian circadian rhythm. Van der Pol oscillator networks have been proposed as a template to produce abstract circuit models that are capable of producing complex oscillatory and spiking patterns of behavior. Here, a particular case of a symmetrically coupled network is treated for its global behavior. It is shown that for a certain connection pattern the circuit is capable of producing globally asymptotically stable oscillations.