Effects of Heterogeneity in Two-Cell Feedforward Networks

TL;DR

This paper investigates how inhomogeneities in two-cell feedforward networks affect their performance, revealing that certain inhomogeneities can enhance output growth despite some adverse effects on signal amplification.

Contribution

It provides a detailed analysis of parameter inhomogeneities in two-cell feedforward networks using bifurcation and singularity theory, highlighting unexpected benefits of inhomogeneity.

Findings

Inhomogeneity in excitation can boost network output growth rate.

Frequency inhomogeneity generally hampers signal amplification.

Phase locking remains robust across various inhomogeneity levels.

Abstract

As the need for higher performance from biological and electronic sensors continues to outpace current technologies, new strategies for designing, developing, and implementing novel sensor systems are emerging. A recently introduced feedforward network-based approach can simultaneously enhance a signal while steering a radiating beam in radio frequency communication systems. Furthermore, the approach is also model-independent, thus making it suitable for other applications. In this work, we aim to understand the effects of inhomogeneities in feedforward arrays, which are inevitable in real-world implementations. We investigate a collection of two-cell feedforward networks composed of pitch-fork cells and Stuart-Landau oscillators and quantify the effects of parameter inhomogeneities using system reduction, analytical and computational bifurcation analyses, and a singularity theory approach. Contrary to common intuition, inhomogeneity in the excitation parameter can be exploited to enhance the network output growth rate. While frequency inhomogeneity in Stuart-Landau networks primarily has an adverse effect on signal amplification, phase locking persists over a surprisingly broad range of inhomogeneity.