Simulated test of electric activity of neurons by using Josephson junction based on synchronization scheme

The chaotic circuit of resistive–capacitive–inductive-shunted Josephson junction is used to simulate behavior of Hindmarsh–Rose neuronal discharges. Based on tracking control theory, the controller contains two gain coefficients was constructed to control the chaotic system of Josephson junction to synchronize the chaotic Hindmarsh–Rose system, and the single controller was approached analytically. The results confirmed that the controller with appropriate gain coefficients was effective to reach complete synchronization (the amplitudes and rhythms of two systems are identical), phase synchronization (rhythms of two systems are identical) of Josephson junction and Hindmarsh–Rose neurons, respectively. The power consumption is estimated in a feasible way. As a result, the electric activities of Hindmarsh–Rose neurons could be simulated by using Josephson junction model completely.

► It suggests that Josephson junction circuit can produce some electric activities of neurons.
► The track control scheme is realize synchronization between the outputs from HR and Josephson junction circuit.
► The application of track control and Lyapunov stability theory are confirmed.
► The power consumption is estimated.