Related papers: Global Exponential Stability for Complex-Valued Re…

Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…

Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…

Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral…

We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…

There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models, indicating how the time elapsed since the last discharge construct the probability density of…

This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…

A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…

We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a…

For the networks that are linear conjugate to complex balanced systems, the delayed version may include two classes of networks: one class is still linear conjugate to the delayed complex balanced network, the other is not. In this paper,…

A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and…

We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…

The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integro-differential equation that describes the collective dynamics…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

We propose a novel {\it Equilibrated Recurrent Neural Network} (ERNN) to combat the issues of inaccuracy and instability in conventional RNNs. Drawing upon the concept of autapse in neuroscience, we propose augmenting an RNN with a…