Related papers: Delayed Dynamics toward Applications
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
We propose here a delay differential equation that exhibits a new type of resonating oscillatory dynamics. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. The…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
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…
Feedback control plays a central role in active matter, yet it is inevitably accompanied by noise and finite perception--action delays. This Perspective reviews recent advances on active systems with delayed interactions, showing how time…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
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…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings…
Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…
We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the…
Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
Analytic, first-principles performance modeling of distributed-memory applications is difficult due to a wide spectrum of random disturbances caused by the application and the system. These disturbances (commonly called "noise") destroy the…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Effect of a complicated many-body environment is analyzed on the chaotic motion of a quantum particle in a mesoscopic ballistic structure. The dephasing and absorption phenomena are treated on the same footing in the framework of a…