Experimental and theoretical investigation of parameter-driven stability and chaos in a non-linear neuron circuit model

In this study, a neural-inspired electronic circuit consisting of a pressure-sensitive FitzHugh-Nagumo model with the addition of a piezoelectric bi-membrane and two capacitors is explored. The governing equations are obtained analytically from Kirchhoff's laws, which represent the nonlinear interactions, oscillatory response, and stability of the circuit. A perturbation term is added to investigate the deviations from the system potential, and the transitions in the system are studied under the assumption of the model. By applying statistical methods and eigenvalue analysis, the parameter space is systematically subdivided and examined, and the results show that the behavior of the system is dominated by divergent behavior, although some periodic oscillatory behavior is seen in certain regions. This highlights the importance of initial conditions and parameter selection on the behavior of the system, which are essential to obtaining stable behavior and developing an efficient control design. Furthermore, an ensemble-size sensitivity analysis is performed to verify the robustness and convergence of the statistical characterization across different numbers of initial conditions. Phase disturbance plots, power spectrum density plots, attractor reconstruction plots, return maps, and noise detection maps are used to analyze the system dynamics. In addition, a multi-sum (multi-parameter interaction) diagram is created to depict the interactions between circuit variables and the overall system behavior.