To reveal how memristive memory, external periodic excitation, and initial-state regulation jointly affect the complex dynamics of a FitzHugh-Nagumo (FHN) neuronal circuit, a multistable memristive FHN neuronal circuit is proposed by replacing the conventional tunnel diode in the classical FHN circuit with a voltage-controlled multistable memristor. First, the multistable memristor model is established from its port current relation and internal state equation. Its memristive and multistable properties are verified through pinched hysteresis loops, state-variable evolution, and responses under different initial conditions. Based on Kirchhoff’s laws, the circuit equations of the proposed neuron are then derived and transformed into an equivalent dimensionless model by voltage, current, and time scaling, which provides a unified framework for stability analysis and numerical simulation. To further clarify the energy regulation mechanism, a dimensionless Hamiltonian energy function is constructed by considering the electric-field energy of the capacitor, the magnetic-field energy of the inductor, and the equivalent electromagnetic energy of the memristive channel. Helmholtz decomposition is used to decompose the vector field into conservative and dissipative components, showing that the introduced multistable memristor provides a state-dependent energy regulation mechanism for the FHN circuit. The effects of external excitation frequency, excitation amplitude, memristive feedback strength, and DC bias on neuronal firing dynamics are systematically investigated using equilibrium distribution, Jacobian eigenvalue analysis, two-dimensional dynamical maps, bifurcation diagrams, Lyapunov exponents, and phase trajectories. Numerical results show that the proposed circuit can generate various firing patterns, including periodic oscillations, bursting oscillations, spiking activity, weakly chaotic oscillations, and chaotic oscillations. In particular, low-frequency excitation promotes time-scale separation between the slow memristive state variable and the fast neuronal variables, thereby inducing pronounced bursting behavior. The bursting transition is jointly governed by stability switching induced by Hopf bifurcations and the unstable equilibrium skeleton shaped by fold bifurcations. Under high-frequency excitation, the system evolves from periodic firing to chaotic firing as the memristive nonlinear feedback strength varies. In addition, since the memristive internal state enters the system through periodic nonlinear functions, the vector field exhibits 2π translational invariance along the memristive state direction. This property enables regular translational displacement of trajectories when only the initial memristive state is changed, leading to multiple coexisting attractors with similar geometric structures but different spatial locations. Basin analysis further shows that the final attractor is mainly determined by the initial memristive state, and the well-defined basin boundaries indicate effective initial-state controllability. Finally, an equivalent PSpice circuit is designed to verify the circuit implementability of the proposed model. The circuit simulation results under different initial voltages of the memristive state capacitor agree well with the numerical results, confirming the initial-state-dependent coexistence and translational displacement of attractors. These results demonstrate that the multistable memristor not only enhances the diversity of firing patterns in the FHN neuronal circuit, but also endows the system with regular multistable coexistence that can be selected by the memristive initial state. The proposed model provides a physically realizable theoretical and circuit framework for studying complex firing regulation, multistable state control, and neuromorphic circuit design based on memristive neurons.