Engineering applications; Graphical modeling frameworks; Input/output behaviors; Localised; Lyapunov-Schmidt reduction methods; Negative conductance; Negative differential conductance; Neuromorphic engineering; Terminal behavior; Ultrasensitive; Control and Systems Engineering; Modeling and Simulation; Control and Optimization
Abstract :
[en] 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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Wel Research Institute, Wavre, Belgium
Besselink, Bart; University of Groningen, Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Groningen, Netherlands ; University of Groningen, Groningen Cognitive Systems and Materials Center (CogniGron), Netherlands
Van Der Schaft, Arjan; University of Groningen, Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Groningen, Netherlands
Language :
English
Title :
Singular networks and ultrasensitive terminal behaviors
Publication date :
2025
Event name :
2025 IEEE 64th Conference on Decision and Control (CDC)
Event place :
Rio de Janeiro, Bra
Event date :
09-12-2025 => 12-12-2025
Audience :
International
Main work title :
2025 IEEE 64th Conference on Decision and Control, CDC 2025
Publisher :
Institute of Electrical and Electronics Engineers Inc.
MathWorks (United States) MERL - Mitsubishi Electric Research Laboratories (United States) Quanser (Canada) SIAM - Society for Industrial and Applied Mathematics
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