Integrative slow effects of memristors induce fast-slow coupled dynamics: a unified modeling framework with hardware...

Despite significant advances in memristive neuron modeling, the physical origin of slow-timescale dynamics and its causal role in governing fast-slow coupled firing behaviors remain insufficiently elucidated-particularly under non-autonomous conditions, where conventional models typically rely on artificially imposed timescale separations. To address this gap, we propose a unified fast-slow modeling framework that exploits the inherent integrative slow dynamics of memristors, rather than artificially assigned time constants, to naturally induce timescale coupling. This framework is instantiated by coupling a flux-controlled memristor as a slow subsystem into the fast Hindmarsh-Rose neuron, yielding a three-dimensional memristive HR (mHR) model in which the small parameter emerges directly from the memristor's physical integration property. Through time-varying equilibrium point analysis, we reveal that periodic bursting originates from reciprocal topological transitions between fold and Hopf bifurcation boundaries, and systematically characterize the modulation laws of external stimulus amplitude and memristive coupling strength via one-dimensional/two-dimensional bifurcation diagrams and Lyapunov exponent spectra. Furthermore, basin-of-attraction calculations confirm the coexistence of chaotic strange attractors and regular limit cycles under identical parameters. These theoretical findings are rigorously validated through both analog circuit simulations (PSpice) and digital hardware implementations on an STM32 platform, with experimental waveforms consistently reproducing the predicted bursting and spiking behaviors. This study establishes a physically grounded theoretical framework for fast-slow memristive neurons and provides a hardware-validated reference for memristor-based neuromorphic engineering applications.