<p>This paper is grounded in the classical FitzHugh–Nagumo (FHN) neuron model. By introducing the memristors and memcapacitors, an improved FHN neuron model based on memristor–memcapacitor coupling (MRMC–FHN) is proposed. This model is designed to enhance the nonlinear dynamic characteristics of the system, simulate the complex behaviors of the neuron, and explore its dynamic characteristics, energy distribution laws, and noise effects. Through scaling the parameters and variables of the model, the circuit equations in dimensionless form and Hamiltonian energy function are derived to verify the energy consistency of the MRMC–FHN model. Methods such as bifurcation analysis, phase diagram analysis, and numerical simulation are used to explore the effects of external current stimulation, memristor gain intensity, and memcapacitor trigger flux on the firing patterns. In addition, to better understand the response mechanism of the neuron in different environments, its discharge behavior in relation to energy consumption is observed in detail. The research findings show that the MRMC–FHN neuron can achieve the transitions between different firing patterns under the dual regulation of the memristor and the memcapacitor, and exhibit corresponding energy consumption situations. Moreover, after introducing Gaussian white noise into the model, the phenomena of stochastic resonance (SR) and coherence resonance (CR) have also been verified.</p>