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We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems…

Optimization and Control · Mathematics 2015-03-09 Nikita Barabanov , Jayant Singh

In this paper, we studied the finite time anti-synchronization of master-slave coupled complex-valued neural networks (CVNNs) with bounded asynchronous time-varying delays. With the decomposing technique and the generalized…

Systems and Control · Electrical Eng. & Systems 2019-10-02 Xiwei Liu , Zihan Li

Absolute exponential stability problem of delay time-varying systems (DTVS) with sector-bounded nonlinearity is presented in this paper. By using the comparison principle and properties of positive systems we derive several novel criteria…

Dynamical Systems · Mathematics 2022-05-19 Nguyen Khoa Son , Nguyen Thi Hong

The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…

Dynamical Systems · Mathematics 2025-04-28 María J. Cáceres , José A Cañizo , Nicolas Torres

This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…

Dynamical Systems · Mathematics 2007-05-23 Matthew M. Peet

This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…

Optimization and Control · Mathematics 2025-12-10 Laurent Baratchart , Sébastien Fueyo , Jean-Baptiste Pomet

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

Analysis of PDEs · Mathematics 2025-07-11 Alhabib Moumni , Cristina Pignotti , Jawad Salhi , Mouhcine Tilioua

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…

Optimization and Control · Mathematics 2025-12-05 Yassine El Gantouh , Yang Liu

In this paper, the stability analysis of quaternion-valued neural networks (QVNNs) with both leakage delay and additive time-varying delays is proposed. By employing the Lyapunov-Krasovskii functional method and fully considering the…

Dynamical Systems · Mathematics 2020-11-03 Qun Huang , Jinde Cao

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough.

Analysis of PDEs · Mathematics 2014-04-18 Fatiha Alabau-Boussouira , Serge Nicaise , Cristina Pignotti

The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly with a delay due to the length of connections.We solve a long…

Analysis of PDEs · Mathematics 2025-03-13 Benoît Perthame , Delphine Salort , Clément Rieutord

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

Dynamical Systems · Mathematics 2010-10-18 M. De La Sen

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem…

Optimization and Control · Mathematics 2023-03-28 Vipin Kumar , Jan Heiland , Peter Benner

This work is devoted to the construction of explicit feedback control laws for the robust, global, exponential stabilization of general, uncertain, discrete-time, acyclic traffic networks. We consider discrete-time, uncertain network models…

Optimization and Control · Mathematics 2016-10-20 Maria Kontorinaki , Iasson Karafyllis , Markos Papageorgiou

For time-delay systems, it is known that global asymptotic stability is guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates in a point-wise manner along solutions, namely whose dissipation rate involves only the…

Optimization and Control · Mathematics 2022-05-17 Iasson Karafyllis , Pierdomenico Pepe , Yuan Wang , Antoine Chaillet

An example of a time-invariant time-delay system that is uniformly globally attractive and exponentially stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals…

Systems and Control · Electrical Eng. & Systems 2024-02-13 Jose L. Mancilla-Aguilar , Hernan Haimovich

To push forward the important emerging research field surrounding multi-area recurrent neural networks (RNNs), we expand theoretically and empirically on the provably stable RNNs of RNNs introduced by Kozachkov et al. in "RNNs of RNNs:…

Machine Learning · Computer Science 2025-08-27 Michaela Ennis , Leo Kozachkov , Jean-Jacques Slotine

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…

Machine Learning · Computer Science 2022-04-27 Uttam Bhat , Stephan B. Munch

In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…

Computer Vision and Pattern Recognition · Computer Science 2016-04-18 Stephan Zheng , Yang Song , Thomas Leung , Ian Goodfellow

The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where…

Chaotic Dynamics · Physics 2022-03-16 Md Sayeed Anwar , Sarbendu Rakshit , Dibakar Ghosh , Erik M. Bollt