UCSD

Mechanical and Aerospace Engineering

• Home
• Publications
• Group
• Teaching
• Software
• Lab

---

Timescale limits of linear-threshold networks
W. Retnaraj, S. Betteti, A. Davydov, F. Bullo, J. Cortés
Proceedings of the IEEE Conference on Decision and Control, Honolulu, Hawaii, 2026, submitted

Abstract

Linear-threshold networks (LTNs) capture the mesoscale behavior of interacting populations of neurons and are of particular interest to control theorists due to their dynamical richness and relative ease of analysis. The aim of this paper is to advance the study of global asymptotic stability in LTNs with asymmetric neural interactions and heterogeneous dissipation under the structural Lyapunov stability condition (LDS). Towards this aim, we introduce a one-parameter family of LTNs that preserves the LDS condition and has a parameter-independent equilibrium set. In the fast limit, this family converges to a projected dynamical system (PDS), while in the slow limit, it converges to a discontinuous hard-selector system (HSS). Under LDS, we prove that the fast PDS limit is globally exponentially stable and that the HSS limit is globally asymptotically stable. This alignment suggests that the limiting systems capture the essential mechanisms governing stability across the entire LTN family. Together with numerical evidence, these findings indicate that resolving stability at the fast and slow endpoints provides a promising and structurally grounded path toward establishing global stability for all LTNs with biologically plausible recurrence and diagonal dissipation.

pdf

Mechanical and Aerospace Engineering, University of California, San Diego
9500 Gilman Dr, La Jolla, California, 92093-0411

Ph: 1-858-822-7930
Fax: 1-858-822-3107

cortes at ucsd.edu
Skype id: jorgilliyo