Related papers: A dichotomy for a class of cyclic delay systems
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
We investigate the dynamical behavior of pull-back trajectories for nonautonomous stochastic feedback systems with multiplicative noise. We proved that there exists a random periodic solution of this system and all pull-back trajectories…
Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this paper we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems…
The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are…
An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters…
The paper investigates some basic dynamical properties of a general system obtained from the Lorenz system using a non-linear feedback controller. We focus on the bifurcation of the equilibrium points and on the existence and the…
In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria is possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the…
Feedback control can be used to generate well-determined nonlinear effective potentials in an optical trap, a goal whose applications may range from non-equilibrium thermodynamics to the generation of non-Gaussian states of mechanical…
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
We present an algorithm for a time-delayed feedback control design to stabilize periodic orbits with an odd number of positive Floquet exponents in autonomous systems. Due to the so-called odd number theorem such orbits have been considered…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested…
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a…
We generalize a method of control of chaos which uses delayed feedback at the period of an unstable orbit to stabilize that orbit. The generalization consists of substituting some portion of the nonlinear dynamical system with a delayed…
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…