<p>Memristors are widely applied in the field of neuroscience. Various memristor-based neuron models are established, and their dynamic behaviors are analyzed in detail by researchers. However, research on functional neurons coupled with hybrid memristors is still lacking in the field. This paper investigates the modeling and complex dynamics of a hybrid memristor-coupled neuron. At first, a functional neural circuit is constructed by connecting two memristors and a piezoelectric ceramic in a nonlinear circuit. And then, a five-dimensional neuron model presented by nonlinear differential equations is obtained. Furthermore, the energy function of the neuron model is approached by physical field energy and Helmholtz’s theorem, respectively. Moreover, an energy-controlled parameter scheme is used to explore the adaptive characteristics of a neuron. Finally, the effects of system parameters (particularly external electric field, external magnetic field, and external stimulus) on neuronal firing patterns are explored by employing a suite of nonlinear theoretical methods, including bifurcation diagram (<i>Bd</i>), sampled time series of variable, largest Lyapunov exponent (<i>LLE</i>), and energy proportion distribution. The results confirmed that neurons can generate chaotic and periodic oscillations under the drive of external sound signals, electric fields, and magnetic fields, and can also exhibit random resonance phenomena when disturbed by external noise electric fields and noise magnetic fields. This research not only deepens the understanding of the modeling mechanism between memristor and dynamics in neural systems but also offers a theoretical foundation for the design of memristor-based neuromorphic computing hardware.</p>