Neurodynamics of Different Neurons Based on a Memristor with <i>S</i>-Type and <i>N</i>-Type Locally Active Domains

To explore the implementation of different neurons using one type of Locally Active Memristor (LAM), this paper proposes a novel LAM model featuring two S-type, two N-type, and two C-type Locally Active Domains (LADs). The local activity of the memristor is analyzed via the DC V–I plot. By employing the small-signal analysis method, the small-signal equivalent circuits for the memristor operating within each of the distinct LADs are constructed. By analyzing the inductive and capacitive properties of the memristor in different LADs, two second-order different neurons are constructed. According to the complexity theory, two third-order different neuronal circuits are built to analyze the action potential and possible abnormal neural signals (chaos). Based on the Edge of Chaos (EOC) theory and Hopf bifurcation theorem, the study demonstrates that action potentials and chaos occur near or in the EOC domains, thereby elucidating the underlying physical mechanisms of neuromorphic behavior. Finally, field-programmable gate array (FPGA) simulations are conducted to illustrate spike activities, self-sustained oscillations, and chaos within the second-order and third-order neuronal circuits. The outcomes of the simulated circuits are consistent with the theoretical analysis, thereby validating the proposed model.