In this paper, we study the nonlinear dynamics of a multiplex system consisting of neuronal networks each with an arbitrary number of FitzHugh-Nagumo neurons and intra-connections and delayed couplings. The network contains an autaptic connection formed by the axon of a neuron on its own soma or dendrites. The stability and instability of the network are determined and the existence of bifurcation is discussed. Then, the study turns to validate the theoretical analysis through numerical simulations. Abundant dynamical phenomena of the network are explored, such as coexisting multi-period oscillations and chaotic responses.