Neuron

Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator.

The simultaneous influence of excitatory synaptic stimuli (the tonic AMPA and NMDA currents) on the neuron model with response differentiation is studied. It is shown that different types of neuron activity (rest state, low frequency or high frequency firing) are observed depending on the conductance of the AMPA and NMDA receptors.

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters.

• The biography of van der Pol, history of his equation and supposed precursors.

• The contribution of A.A. Andronov in the theory of self­oscillations.