Related papers: Resonating Delay Equation
In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…
The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law.…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…
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…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
We propose a system of partial differential equations with a single constant delay $\tau > 0$ describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of $\mathbb{R}^{1}$. For an initial-boundary value…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
In the present article we show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing…
We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow-flow using the action-angle (AA) formalism. Exact inversion of the…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and dominates, and determine criteria to characterise this…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…