The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that eigenbranches that develop from the stable Lyapunov exponents of the free system also have a strong influence on the control properties, either by hybridization or by a crossing of branches which interchanges the role of the leading eigenvalue. Our findings are confirmed by numerical analysis of two particular examples, the Toda and the Rossler models. More important is the verification by actual electronic circuit experiments. Here, the observed reduction of control domains can be attributed to these additional eigenvalue branches. The investigations lead to a thorough analytical understanding of the stability properties in time-delayed feedback systems.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/physreve.61.5045 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Development of circadian rhythms in mammalian systems.
Biochem J
December 2024
Department of Pharmacology, Physiology, and Neurobiology, University of Cincinnati College of Medicine, Cincinnati, OH, U.S.A.
In mammals, molecular mechanisms of circadian rhythms involve a time-delayed negative feedback loop generating autonomous oscillations of ∼24 h. Most cell types in mammals possess circadian rhythms regulating temporal organization of cellular and physiological processes. Intriguingly, pluripotent stem cells do not possess circadian rhythms and oscillations arise after a defined period of differentiation.
View Article and Find Full Text PDFHeat production in a stochastic system with nonlinear time-delayed feedback.
Phys Rev E
November 2024
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany.
Using the framework of stochastic thermodynamics we study heat production related to the stochastic motion of a particle driven by repulsive, nonlinear, time-delayed feedback. Recently it has been shown that this type of feedback can lead to persistent motion above a threshold in parameter space [R. A.
View Article and Find Full Text PDFEnergy-based theory of autoresonance in chains of coupled damped-driven generic oscillators.
Phys Rev E
October 2024
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India.
An energy-based theory of autoresonance in driven dissipative chains of coupled generic oscillators is discussed on the basis of a variational principle concerning the energy functional. The theory is applied to chains of delayed Duffing-Ueda oscillators and the equations that together govern the autoresonance forces and solutions are derived and solved analytically for generic values of parameters and initial conditions, including the case of quenched time-delay disorder. Remarkably, the presence of retarded potentials with time-delayed feedback drastically modify the autoresonance scenario preventing the growth of the energy oscillation over specific regions of the parameter space.
View Article and Find Full Text PDFFeedback driven autonomous cycles of assembly and disassembly from minimal building blocks.
Nat Commun
November 2024
Department of Chemical Sciences and Centre for Advanced Functional Materials, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, 741246, India.
The construction of complex systems by simple chemicals that can display emergent network dynamics might contribute to our understanding of complex behavior from simple organic reactions. Here we design single amino acid/dipeptide-based systems that exhibit multiple periodic changes of (dis)assembly under non-equilibrium conditions in closed system, importantly in the absence of evolved biocatalysts. The two-component based building block exploits pH driven non-covalent assembly and time-delayed accelerated catalysis from self-assembled state to install orthogonal feedback loops with a single batch of reactants.
View Article and Find Full Text PDFDynamical analysis and fault detection application of a time-delayed multi-stable stochastic resonance system driven by white correlated noises.
Sci Rep
October 2024
School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China.
Bearing fault diagnosis is a crucial means to ensure the normal operation of machinery, reduce maintenance costs, enhance equipments safety and extend the service life of bearings. However, the noise interference in input signals often affects the effective extraction of bearing fault signals. In this paper, a time-delay multi-stable stochastic resonance (SR) system driven by white correlated noises is proposed.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!