Yiğit Aydoğan, Elham Minayi
The bang-bang adaptive law of a periodically forced memristive FitzHugh-Nagumo (FHN) circuit is replaced with a continuous energy-feedback controller formulated in a hardware-realizable form using the Add-Differentiate integrated circuit (AD-IC) proportional-integral-derivative architecture. The architecture is operated in the proportional limit (Ti = 109 and Td = 0), so the switching dynamics are governed by the proportional gain Kp while retaining a mapping to the AD-IC resistor ratio. Promoting the diversion-branch conductance parameter λ5 from a fixed scalar to a dynamical state driven by the controller output yields a six-dimensional closed-loop system. In the quasi-static limit, where λ5 evolves slowly relative to the FHN oscillation period, the time to drive the circuit from its high-energy firing mode to the quiescent low-energy state satisfies the semi-analytical relation τswitch=I(H∗)/Kp, where H∗ is the target energy and I(H∗) is an energy-landscape path integral evaluated numerically from quasi-static steady-state measurements. For a selected target, the inverse dependence on Kp = R1/R2 gives a closed-form gain-scaling rule that separates component selection from the application energy target. A feasibility boundary Hmax∗≈1.87 emerges from the minimum of the energy landscape along the approach path to the fold bifurcation; a two-branch bifurcation diagram confirms the wide bistable region in which both the firing mode and the quiescent mode coexist as stable attractors. Validation against 15 Runge-Kutta simulations across a two-dimensional (Kp,H∗) design space gives a mean absolute error of 14.7%, with systematic overestimation attributed to forcing-induced advance of the transition relative to the quasi-static fold point at larger gains.