The capacitive property of biological neuronal membranes makes capacitors essential for constructing neural circuits. Connecting different nonlinear elements in parallel to simulate the diversity of ion channels has become a key issue in developing functional neuron models. This paper uses nonlinear elements to couple multiple capacitors, mimicking the multilayer membrane structure of biological cells. It investigates the membrane potential dynamics and the decisive role of memory effects in the system's frequency conversion capability. Results show that the dual-nonlinear-resistor configuration cannot generate frequency doubling or division under any parameter settings. The three capacitors always lock to the driving frequency. In contrast, the single-memristor configuration stably outputs subharmonic phase locking over a wide parameter range. The system's average energy increases monotonically with the memristor parameter. When the driving frequency changes, the system presents a continuous rational phase-locking ladder from frequency doubling to deep frequency division. Among these states, the 5/8 division state achieves the best balance between energy efficiency and signal stability. This division state is a global attractor, and the system is insensitive to initial conditions. The interlayer capacitance ratio and the inductance parameter are key factors for maintaining the phase-locked state. This work integrates frequency conversion, energy storage, and multi-port output into a single circuit. It provides theoretical basis and engineering guidance for the functional design of nonlinear circuits.