Multilevel regularity of orbits of expanding Lorenz maps with application to the Courbage-Nekorkin-Vdovin model

We discuss the structure and properties of itineraries of periodic orbits for expanding Lorenz maps with nontrivial rotation interval. In particular, it is shown that periodic orbits of such maps are organized in two cascades (called Stern-Brocot and Geller-Misiurewicz cascades), which are closely related to the Farey tree of rational rotation numbers of a given map. The obtained results are illustrated with a reduced Courbage-Nekorkin-Vdovin neuron model, allowing us to characterize regularity of periodic spiking patterns in the model.