As a nonlinear memory device, the memristor is often used as a circuit load. In this paper, a nonlinear memory system based on a traditional current-mode Cuk converter with a voltage-controlled memristor is constructed. By deducing the state equation of circuit topology and the continuous current mode state equation, the simulation model is constructed. The dynamic characteristics of the system are explored by using a sequence diagram, phase diagram and bifurcation diagram. In addition, parametric resonance micro perturbation is introduced to suppress the chaos of the system. Finally, by using PYTHON and PSIM for simulation, the results verify the dynamic characteristics of the system and the effectiveness of the control method.