Neural dynamics modelled by one-dimensional circle maps

The single Bonhoeffer-van der Pol (BvP) neuron, driven by a sinusodial external stimulus shows periodic, quasiperiodic and chaotic states. Frequency-lockings, followed by period doubling cascades to chaos, suggest a relation to the universal behaviour of one-dimensional circle maps. We present a method to describe the membrane potential activity of single neurons with a circle map. Furthermore, we show that this equivalence can be found in networks of coupled BvP elements. In dependence of the interaction strength we always observe a region, where a stimulus-induced synchronization can be understood in terms of coupled one-dimensional circle maps.