Dynamics and DSP implementation of a wide-range locally active memristor-coupled Aihara neuron

In neuromorphic computing, constructing bionic devices for artificial neuronal communication is a key research direction. This paper proposes a novel discrete locally active memristor (LAM) model characterized by a sinusoidal state equation. The pinched hysteresis loop, power-off plot, and direct current voltage-current curve are employed to verify its memristive fingerprints, non-volatility, and local activity, respectively. Notably, the locally active region expands with the magnetic flux range. The LAM is then coupled as a self-connecting synapse into the Aihara neuron, establishing the LAM-Aihara map. Using bifurcation diagrams, Lyapunov exponent spectra, equilibrium point analysis and other standard nonlinear analysis tools to characterize dynamical behaviors, we identify three novel dynamical features of the LAM-Aihara map: triangular waveform bursting firings, centrosymmetric coexisting attractors under different initial conditions, and a high spectral entropy reaching 0.93. The physical realizability of the map is further validated on a digital signal processing platform. These findings provide theoretical and experimental support for employing memristive single neuron coupling in the field of information encryption.