<p>DC-DC converters are widely used in power electronics but exhibit complex nonlinear behaviors that depend strongly on circuit parameters and load characteristics, making modeling and control particularly challenging. This paper presents a detailed dynamic analysis of a three-level flying capacitor boost converter, extended by integrating a parallel memristive load. Rather than a simple load substitution, the memristive element introduces memory-dependent nonlinearities, significantly altering the system’s dynamic response and necessitating the development of a tailored modeling framework. The proposed model builds upon the converter topology introduced by Hung Chi and Che Yu (2018), but redefines the system behavior by incorporating a two-state (ON/OFF) switching mechanism governed by a reset flip-flop (RS), influenced by a dual closed-loop voltage–current controller and a periodic modulation signal. This configuration enables the emergence of complex dynamic patterns, including bifurcation sequences, periodic windows, and chaotic regimes. The originality of this work lies in the way memristive nonlinearity interacts with multi-level switching, altering the converter’s global behavior in a nontrivial way that challenges conventional control strategies and requires dedicated system-level modeling and stabilization approaches. Simulation results including bifurcation diagrams, phase portraits, and time domain waveforms reveal a rich set of behaviors, highlighting the system’s capacity for stable and controlled operation under varying conditions. Furthermore, the consistency between numerical simulations and PSIM results supports the validity and applicability of the proposed modeling and analysis approach in practical converter design.</p>