We consider a chemostat-type model in which a single species feeds on a limiting nutrient supplied at a constant rate. The model incorporates a general nutrient uptake function and two distributed (infinite) delays. The first delay models the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition, and the second delay indicates that the growth of ...

We consider a model of game-theoretic learning based on online mirror descent (OMD) with asynchronous and delayed feedback information. Instead of focusing on specific games, we consider a broad class of continuous games defined by the general equilibrium stability notion, which we call λ-variational stability. Our first contribution is that, in this class of games, the actual sequence of play ...

Recently, a large number of neural networks models have been proposed and studied extensively since Hopfield constructed a simplified neural network. In most networks however, it is usually expected that time delays exist during the processing and transmission of signals. In general, delay-differential equations exhibit much more complicated dynamics than ordinary differential equations since a...

In this paper, based on SIR and SEIR epidemic models with a general nonlinear incidence rate, we incorporate time delays into the ordinary differential equation models. In particular, we consider two delay differential equation models in which delays are caused (i) by the latency of the infection in a vector, and (ii) by the latent period in an infected host. By constructing suitable Lyapunov f...

Abstract. We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular w...

Part IT deals with the design problem of generalized linear controllers for linear systems with after-effect so that the resulting closed-loop system is globally uniformly asymptotically stable in the Lyapunov's sense. The controllers are universal in the sense that they include the usual delays (namely, point, distributed and mixed point-distributed delays) which can be finite, infinite or eve...

Existing works on ABR feedback control design basically neglected the eeect of multiple feedback loop delays and high-priority CBR/VBR traac transmission. With multiloop delays, the already existing low-frequency high-magnitude oscillations of ABR traac within each loop can become much worsened. With CBR/VBR priority traac, the original control stability conditions can be ruined. This paper pro...

The timetable information problem can be solved by computing shortest paths in special graphs built from timetable data. In general, two models exist: the time-dependent and time-expanded network. In a recent work, both models are compared with respect to advantages and disadvantages on a theoretical and a practical framework. In addition, an extensive experimental evaluation reveals further di...

Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug...

We obtain global stability lobes of two models of turning processes with inherit nonsmoothness due to the presence of state-dependent delays. In the process, we transform the models with state-dependent delays into systems of differential equations with both discrete and distributed delays and develop a procedure to determine analytically the global stability regions with respect to parameters....