Second-order memristor-coupled heterogeneous neuron model: multi-attractor, multi-stability, and hardware...

Memristor-based neuron models offer a promising framework for reproducing biologically inspired firing activities and realizing neuromorphic hardware. In this work, we develop a heterogeneous neuron model by introducing a second-order memristor (SOM) synapse that couples a Tabu learning neuron (TLN) and a FitzHugh-Nagumo (FHN) neuron. A novel SOM model is first proposed and shown to possess dual-memory characteristics, providing richer state-dependent regulation than conventional first-order memristors. By exploiting this enhanced memory mechanism, the SOM functions as an adaptive nonlinear synapse that substantially enriches the dynamical repertoire of the coupled neuronal system. The proposed model exhibits a wide range of complex behaviors, including chaos, hyperchaos, coexisting attractors, multistability, and intricate multi-butterfly attractors. Comprehensive nonlinear analyses based on bifurcation diagrams, Lyapunov exponent spectra, entropy complexity measures, attraction basins, and the 0-1 chaos test reveal the underlying dynamical evolution. Remarkably, the SOM parameters can flexibly regulate the number and distribution of coexisting butterfly attractors, whereas minute perturbations of the memristor initial states lead trajectories toward distinct asymptotic states, demonstrating extreme sensitivity and memory-dependent state selection. These findings uncover a previously unexplored mechanism through which higher-order memristive memory shapes heterogeneous neuronal dynamics. To validate the theoretical results, an analog circuit implementation of the proposed model is developed. Both circuit simulations and FPGA-based hardware experiments successfully reproduce the predicted dynamical phenomena, confirming the physical realizability and robustness of the proposed neuron model. The results highlight the potential of second-order memristive synapses for constructing highly reconfigurable neuromorphic systems and advancing the understanding of memory-induced cognitive neurodynamics.