Related papers: Wada property in systems with delay
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…
This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.
Action-feedback delay during operation reduces both task performance and sense of agency (SoA). In this study, using information-theoretic free energy, we formalized a novel mathematical model for explaining the influence of delay on both…
We study the structure of the set of harmonic solutions to perturbed nonautonomous, T-periodic, separated variables ODEs on manifolds. The perturbing term is allowed to contain a finite delay and to be T-periodic in time.
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
The discovery of topological insulators has opened new prospects for robust signal transport for electronic, phononic, and photonic devices. Though transport of topological protected edge states is robust to disorder, large fluctuations and…
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…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be…
We introduce the map representation of a time-delayed system in the presence of delay time modulation. Based on this representation, we find the method by which to analyze the stability of that kind of a system. We apply this method to a…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…
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 derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spin- like systems, which is the case when…