Dynamical and Stochastic Analysis of a Piezoelectric Neuron Model for Intelligent Sensing Applications.

In this work, we explore a piezoelectric neuron model in deterministic perturbations and stochastic forcing due to its use in mechanically driven sensing systems and neuromorphic sensor design. The model comprises of fast activation and slow recovery behaviors and constitutes a multiscale excitable system, converting external mechanical perturbations into nonlinear electrical responses. We initially examine the deterministic dynamics with phase-space reconstruction, basin of attraction mapping, return map analysis and sensitivity to initial conditions. These findings demonstrate stable limit-cycle oscillations and high nonlinear sensitivity that are crucial to high-resolution sensing and signal amplification. Stochastic forcing is added in order to include realistic environmental effects, and solved numerically with the Euler-Maruyama scheme. Time-series statistics, phase portraits, and recurrence quantification analysis are used to analyze the resulting ensemble dynamics, making it possible to characterize the variability and loss of predictability caused by noise. Comparison of deterministic and stochastic regimes indicates that the intensity of noise can considerably alter the firing patterns and recurrence structures.