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Singular networks and ultrasensitive terminal behaviors

Year: 2025

Type: conference-paper

Abstract: Negative conductance elements are key in shaping the input-output behavior at the terminals of a network through localized positive feedback amplification. The balance of positive and negative differential conductances creates singularities at which rich, intrinsically nonlinear, and ultrasensitive terminal behaviors emerge. Motivated by neuromorphic engineering applications, in this note we extend a recently introduced nonlinear network graphical modeling framework to include negative conductance elements. We use this extended framework to define the class of singular networks and to characterize their ultrasensitive input-output behaviors at given terminals. Our results are grounded in the Lyapunov-Schmidt reduction method, which is shown to fully characterize the singularities and bifurcations of the input-output behavior at the network terminals, including when the underlying input-output relation is not explicitly computable through other reduction methods.

Source: Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes

DOI: 10.1109/cdc57313.2025.11312852

Authors: Alessio Franci, Bart Besselink, Arjan van der Schaft

Institution: University of Groningen

Language: English

Topic: Advanced Memory and Neural Computing

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7123345389

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