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Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the…

Dynamical Systems · Mathematics 2022-03-29 Thomas Chaffey

We discuss the synchronization of coupled neurons which are modelled as FitzHugh-Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting…

Chaotic Dynamics · Physics 2008-09-05 Philipp Hoevel , Markus A. Dahlem , Eckehard Schoell

For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

We study the dynamics of two neuronal populations weakly and mutually coupled in a multiplexed ring configuration. We simulate the neuronal activity with the stochastic FitzHugh-Nagumo (FHN) model. The two neuronal populations perceive…

Adaptation and Self-Organizing Systems · Physics 2021-03-17 M. Masoliver , C. Masoller , A. Zakharova

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that…

Disordered Systems and Neural Networks · Physics 2017-08-16 Clement Zankoc , Duccio Fanelli , Francesco Ginelli , Roberto Livi

We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain…

Optimization and Control · Mathematics 2021-07-29 Andrii Mironchenko , Christoph Kawan , Jochen Glück

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all…

Dynamical Systems · Mathematics 2015-10-07 Niloofar Farajzadeh Tehrani , MohammadReza Razvan

This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…

Optimization and Control · Mathematics 2014-09-29 Ian R. Manchester , Jean-Jacques E. Slotine

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…

Machine Learning · Computer Science 2026-03-18 Hiroyasu Tsukamoto , Soon-Jo Chung , Jean-Jacques E. Slotine

We describe the fast-slow dynamics of two FitzHugh--Nagumo equations coupled symmetrically through the slow equations. We use symmetry arguments to find a non-empty open set of parameter values for which the two equations synchronise, and…

Dynamical Systems · Mathematics 2025-07-24 Bruno F. F. Gonçalves , Isabel S. Labouriau , Alexandre A. P. Rodrigues

We solve a conjecture on multiple nondegenerate steady states, and prove bistability for sequestration networks. More specifically, we prove that for any odd number of species, and for any production factor, the fully open extension of a…

Dynamical Systems · Mathematics 2019-06-04 Xiaoxian Tang , Jie Wang

We study local stabilization of nonlinear control systems under explicit gain constraints on the feedback law. Using a quantitative refinement of Brockett's openness condition, we introduce the notion of a maximal continuous openness rate…

Optimization and Control · Mathematics 2026-02-23 Bryce Christopherson , Farhad Jafari

Multiplex networks are networks composed of multiple layers such that the number of nodes in all layers is the same and the adjacency matrices between the layers are diagonal. We consider the special class of multiplex networks where the…

Adaptation and Self-Organizing Systems · Physics 2021-06-25 Rico Berner , Volker Mehrmann , Eckehard Schöll , Serhiy Yanchuk

A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to…

Optimization and Control · Mathematics 2007-05-23 Brian Ingalls , Eduardo D. Sontag

A spin system can be thought of as an information coding system that transfers information of the interaction configuration into information of the equilibrium state of the spin variables. Hence it can be expected that the relations between…

Disordered Systems and Neural Networks · Physics 2020-10-21 Tatsuto Murayama , Asaki Saito , Peter Davis

This paper investigates the existence of an equilibrium point in multiterminal HVDC (MT-HVDC) grids, assesses its uniqueness and defines conditions to ensure its stability. An offshore MT-HVDC system including two wind farms is selected as…

Signal Processing · Electrical Eng. & Systems 2018-10-31 Santiago Sanchez , Alejandro Garces , Gilbert Berna , Elisabetta Tedeschi

Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for a network of infinitely many systems, termed as infinite networks. The proposed small-gain theorem addresses…

Dynamical Systems · Mathematics 2020-02-18 Navid Noroozi , Andrii Mironchenko , Christoph Kawan , Majid Zamani

We undertake a fundamental study of network equilibria modeled as solutions of fixed point equations for monotone linear functions with saturation nonlinearities. The considered model extends one originally proposed to study systemic risk…

Dynamical Systems · Mathematics 2021-01-19 Leonardo Massai , Giacomo Como , Fabio Fagnani

We consider a non-reciprocically coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour, a suppression of coarsening as well as the existence of localised states. Here, after introducing the model we…

Pattern Formation and Solitons · Physics 2023-08-11 Tobias Frohoff-Hülsmann , Uwe Thiele , Len M. Pismen

We consider time-invariant nonlinear $n$-dimensional strongly $2$-cooperative systems, that is, systems that map the set of vectors with up to weak sign variation to its interior. Strongly $2$-cooperative systems enjoy a strong…

Dynamical Systems · Mathematics 2026-01-09 Rami Katz , Giulia Giordano , Michael Margaliot