Numerically induced bursting in a set of coupled neuronal oscillators

•We model two coupled FitzHugh–Nagumo neurons.•Numerical integration with insufficient precision recovers a bursting state.•We investigate the mechanism behind the onset of spurious bursting.

We present our numerical observations on dynamics in the system of two linearly coupled FitzHugh–Nagumo oscillators close to the destabilization of the state of rest. Under the considered parameter values the system, if integrated sufficiently accurately, converges to small-scale periodic oscillations. However, minor numerical inaccuracies, which occur already at the default precision of the standard Runge–Kutta solver, lead to a breakup of periodicity and an onset of large-scale aperiodic bursting.