Related papers: A Discrete-Time, Time-Delayed Lur'e Model with Bia…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
Using a new implicit discretization scheme, we study in this paper the existence and uniqueness of strong solutions for a class of Lur'e dynamical systems where the set-valued feedback depends on both time and state. This work is a…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a…
Oscillations represent a ubiquitous phenomenon in biological systems. The conventional models of biological periodic oscillations are usually proposed as interconnecting transcriptional feedback loops. Some specific proteins function as…
This work addresses fundamental issues related to the structure and conditioning of linear time-delayed models of non-linear dynamics on an attractor. While this approach has been well-studied in the asymptotic sense (e.g. for infinite…
The interplay of positive and negative feedback loops on different time scales appears to be a fundamental mechanisms for robust and tunable oscillations in both biological systems and electro-mechanical systems. We develop a detailed…
We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling…
The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
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…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
In this paper we develop novel results on self triggering control of nonlinear systems, subject to perturbations and actuation delays. First, considering an unperturbed nonlinear system with bounded actuation delays, we provide conditions…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in…
We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We…