A remark on incoherent feedforward circuits as change detectors and feedback controllers

TL;DR

This paper investigates incoherent feedforward loops in signal processing and control, revealing that stabilization depends on specific parameter regions, with variations including positive self-feedback and negative feedback configurations.

Contribution

It provides a detailed analysis of IFFL response properties to exponential inputs and explores stability conditions in different feedback configurations.

Findings

Stabilization occurs only in disconnected parameter regions.

Positive self-feedback affects the response dynamics.

Negative feedback configurations can serve as controllers.

Abstract

This note analyzes incoherent feedforward loops in signal processing and control. It studies the response properties of IFFL's to exponentially growing inputs, both for a standard version of the IFFL and for a variation in which the output variable has a positive self-feedback term. It also considers a negative feedback configuration, using such a device as a controller. It uncovers a somewhat surprising phenomenon in which stabilization is only possible in disconnected regions of parameter space, as the controlled system's growth rate is varied.