The dynamics of memristive device in response to neuron-like signals and coupling electronic neurons via memristive device has been investigated theoretically and experimentally. The simplest experimental system consists of electronic circuit based on the FitzHugh-Nagumo model and metal-oxide memristive device. The hardware-software complex based on commercial data acquisition system is implemented for the imitation of signal from presynaptic neuron`s membrane and synaptic signal transmission between neurons. The main advantage of our system is that it uses real time dynamics of memristive device. Electrical response of memristive device shows its behavioral flexibility that allows presenting a memristive device as an active synapse. This means an internal adjustment of the parameters of memristive device that leads to modulation of neuron-like signals. Physics-based dynamical model of memristor is developed in MATLAB for numerical simulation of such a memristive interface to describe and predict experimentally observed regularities of synchronization of neuron-like oscillators. FitzHugh-Nagumo circuits time series with a linear or stepwise increase in the signal amplitude are used to study the memristor response and coupling of neuron-like oscillators taking into account the stochasticity of memristor model to compare the numerical and experimental data. The observed forced synchronization modes characterize the dynamic complexity of the memristive device, which requires further description using high-order dynamical models. The developed memristive interface will provide high efficiency in the imitation of the synaptic connection due to its stochastic nature and can be used to increase the flexibility of neuronal connections for neuroprosthetic challenges.