<p>The extreme complexity and diversity of real biological synaptic environments necessitate simulating synaptic heterogeneity and complex synaptic interactions and constructing neural networks with high biological realism. In this paper, a novel second-order memristor is proposed, taking into account neural synaptic heterogeneity, electromagnetic radiation, and synaptic current crosstalk during dendritic integration. By combining a two-dimensional Hindmarsh–Rose (HR) neuron with two Hopfield neurons, a hybrid-order memristive synaptic current crosstalk-coupled heterogeneous neural network (HMSCC-HNN) model based on second-order and first-order memristors is innovatively constructed. The hidden dynamical behaviors of the system are comprehensively analyzed by phase portraits, time series, multidimensional bifurcation diagrams, Lyapunov exponent spectra, and basins of attraction. The results show that the introduction of hybrid-order memristive synaptic current crosstalk greatly enriches the dynamics of the heterogeneous neural network and enables the system to generate complex hidden dynamical behaviors without equilibrium points. Further studies reveal that the coupling strengths and synaptic current crosstalk strengths play significant roles in regulating firing activities, and various firing patterns, including periodic spiking, chaotic bursting, and refractory bursting, can be obtained by adjusting these parameters. In addition, under the combined influence of coupling strengths and synaptic current crosstalk strengths, the system exhibits rich antimonotonicity, state transition, and multistable coexisting firing phenomena. Finally, an analog circuit of the HMSCC-HNN system is designed, and its feasibility and practical value are verified by PSpice simulations and STM32F407ZGT6 microcontroller-based hardware experiments.</p>