Dynamics of memristive circuit driven by Josephson junction

The nonlinear circuit with charge-controlled memristor (CCM) can capture the external electric field effect. The nonlinear circuit with Josephson junction (JJ) can estimate the external magnetic field effect. Therefore, we propose an enhanced functional circuit by connecting a CCM and a JJ into a simple RLC nonlinear circuit. This enchanced circuit can estimate the external electromagnetic fields concurrently. The dynamical equations of the new memristive circuit and its Hamilton energy function are obtained by using the Kirchhoff's law and the Helmholtz's theorem. Furthermore, the complex dynamics of memristive circuit are investigated by applying bifurcation diagrams, Lyapunov exponents and time sampled series. The simulation experiment results indicate that the electromagnetic field has a great influence on complex dynamics of memristive circuit. In fact, this new nonlinear circuit is also a functional neural circuit, and it can be used to study the collective dynamic of functional neural network under the condition of an external electromagnetic fields.