Analog Realization and Measurement of a Forced Aliev-Panfilov Excitable Oscillator

Abstract

A single resistor moves a discrete analog realization of the forced Aliev-Panfilov excitable oscillator from a chaotic operating point of the model to a regular one. In this model a rate parameter multiplies the complete right-hand side of the excitation equation, forcing term included. The input resistor of the excitation integrator sets that parameter, so no state, delay element, or controller is added. Sampled waveforms were recorded at two resistor values, with two independent runs each. The measured excitation excursion agrees with numerical integration to within three percent at the baseline setting and five percent at the rate-controlled setting. Between the two settings the excitation excursion contracts by a factor of thirteen. At the rate-controlled setting the recovery excursion exceeds prediction by a factor of eight. This excess traces to a displaced operating point on the state-dependent recovery rate. Thermal drift in the multiplier chain and leakage at the high-impedance recovery-rate divider could each produce it, and the present data do not separate them. A tested bipolar input stage strongly loads that divider, a constraint absent from the ideal equations. The divider, not the sub-hertz signal bandwidth, sets the amplifier input-stage requirement.