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We investigated the dynamic processes in a superconducting neuron based on Josephson contacts without resistive shunting (S_C-neuron). Such a cell is a key element of perceptron-type neural networks that operate in both classical and quantum modes. The analysis of the obtained results allowed us to find the mode when the transfer characteristic of the element implements the “sigmoid” activation function. The numerical approach to the analysis of the equations of motion and the Monte Carlo method revealed the influence of inertia (capacitances), dissipation, and temperature on the dynamic characteristics of the neuron.