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We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In…

Molecular Networks · Quantitative Biology 2007-05-23 Konstantin Klemm , Stefan Bornholdt

Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…

Systems and Control · Electrical Eng. & Systems 2020-05-12 Markus Tranninger , Richard Seeber , Martin Steinberger , Martin Horn

This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Hao Yin , Bayu Jayawardhana , Stephan Trenn

In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…

Dynamical Systems · Mathematics 2021-07-08 William Duncan , Tomas Gedeon , Hiroshi Kokubu , Konstantin Mischaikow , Hiroe Oka

The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…

Optimization and Control · Mathematics 2024-10-15 Alhabib Moumni , Mohamed Mehdaoui , Jawad Salhi , Mouhcine Tilioua

Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…

Optimization and Control · Mathematics 2025-03-04 Yuhao Zhang , Xiangru Xu

We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…

Analysis of PDEs · Mathematics 2015-06-17 Serge Nicaise , Cristina Pignotti

This paper treats the global stabilization problem of continuous-time switched affine systems that have rank-deficient convex combinations of their dynamic matrices. For these systems, the already known set of attainable equilibrium points…

Optimization and Control · Mathematics 2022-04-15 Lucas N. Egidio , Grace S. Deaecto , Raphaël M. Jungers

In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…

Optimization and Control · Mathematics 2020-02-18 Ihab Haidar , Yacine Chitour , Paolo Mason , Mario Sigalotti

Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to…

Systems and Control · Electrical Eng. & Systems 2021-09-08 Mohammadreza Doostmohammadian , Usman A. Khan , Mohammad Pirani , Themistoklis Charalambous

Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…

Chaotic Dynamics · Physics 2024-06-11 Jordan Culp , Wilten Nicola

The success of neural networks across most machine learning tasks and the persistence of adversarial examples have made the verification of such models an important quest. Several techniques have been successfully developed to verify…

Machine Learning · Computer Science 2019-10-14 Nathanaël Fijalkow , Mohit Kumar Gupta

The elapsed time equation is an age-structured model that describes the dynamics of interconnected spiking neurons through the elapsed time since the last discharge, leading to many interesting questions on the evolution of the system from…

Analysis of PDEs · Mathematics 2025-07-15 Mauricio Sepulveda , Nicolas Torres , Luis Miguel Villada

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Dynamical Systems · Mathematics 2007-07-03 Matthew M. Peet , Antonis Papachristodoulou , Sanjay Lall

We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology…

Multiagent Systems · Computer Science 2024-09-16 Nana Wang , Esteban Restrepo , Dimos V. Dimarogonas

We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…

Analysis of PDEs · Mathematics 2014-03-10 Jean-Michel Coron , Hoai-Minh Nguyen

The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…

Dynamical Systems · Mathematics 2019-07-24 Cinzia Elia , Ismael Maroto , Carmen Núñez , Rafael Obaya

This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…

Optimization and Control · Mathematics 2018-06-22 Yao Liqiang , Zhang Weihai

For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…

Dynamical Systems · Mathematics 2009-11-13 Marc Timme , Fred Wolf

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at…

Systems and Control · Electrical Eng. & Systems 2023-10-30 Mohammadreza Doostmohammadian , Alireza Aghasi , Maria Vrakopoulou , Hamid R. Rabiee , Usman A. Khan , Themistoklis Charalambou