Related papers: Operon Dynamics with State Dependent Transcription…
We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…
We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and without recurrent dynamics. With state dependent delay…
We investigate the consequences of periodic, on-off glucose infusion on the glucose-insulin regulatory system on the basis of a system-level mathematical model with two explicit time delays. Studying the effects of such infusion protocols…
Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero.…
We consider the two-component delay system $\varepsilon x^{\prime}(t)=-x(t)-y(t)+f(x(t-1)),$ $y^{\prime}(t)=\eta x(t)$ with small parameters $\varepsilon,\eta$, and positive feedback function $f$. Previously, such systems have been reported…
In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…
A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…
We study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…
The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
Delay is an inherent feature of genetic regulatory networks. It represents the time required for the assembly of functional regulator proteins. The protein production process is complex, as it includes transcription, translocation,…
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
Model-free algorithms are brought into the control system's research with the emergence of reinforcement learning algorithms. However, there are two practical challenges of reinforcement learning-based methods. First, learning by…
We study the spatio-temporal dynamics of the generalized repressilator, a system of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a cascade of unstable periodic orbits…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
This paper studies data-driven control of unknown sampled-data systems with communication delays under an event-triggering transmission mechanism. Data-based representations for time-invariant linear systems with known or unknown system…
We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this…
We propose a novel feedback controller for a class of uncertain higher-order nonlinear systems, subject to delays in both state measurement and control input signals. Building on the prescribed performance control framework, a…
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse,…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…