Related papers: Delay, resonance and the Lambert W function
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
In this paper, we give explicit exponential estimates $\displaystyle |x(t)|\leq M e^{ -\gamma (t-t_0) }$, where $t\geq t_0$, $M>0$, for solutions of a linear scalar delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit expression for approximating the rate change is provided,…
We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…
Metastable decay exhibits a familiar exponential regime bracketed by early-time deviations and late-time power-law tails. We adopt the real-time, flux-based definition of the decay rate in the spirit of Andreassen et al.\ direct method and…
We report evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is {\em not}, in fact, slow. Instead nonlinear transfers lead to evolution time scales that are smaller than one wave…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
This Report discusses a recently developed concept of Limiting Phase Trajectories (LPTs) providing a unified description of resonant energy transport in a wide range of classical and quantum dynamical systems with constant and time-varying…
We investigate the Coulomb blockade resonances and the phase of the transmission amplitude of a deformed ballistic quantum dot weakly coupled to leads. We show that preferred single--particle levels exist which stay close to the Fermi…
The goal of our work is to investigate the oscillation and asymptotic properties of a class of difference equations with a condition. In contrast to most previous studies, the oscillation of the investigated equation is obtained with only…
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…
We study solutions of a transcendental equation for the complex chemical potential at which a random-matrix QCD model can undergo a phase transition at zero mass. An explicit solution is obtained in terms of the Lambert W function. We also…
In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network. Our work is motivated by novel applications from the domain of process automation, Machine-Type Communication…
Laser has unique advantages such as abundant spectrum resources and low propagation divergence in wireless charging and wireless communications, compared with radio frequency. Resonant beams, as a kind of intra-cavity laser beams, have been…
We consider a generic description of interacting dynamical Dark Energy, characterized by an equation of state with a time dependent coefficient $w(t)$, and which may interact with both radiation and matter. Without referring to any…
Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…
The Majorana resonant level model (MRLM) describes the universality class of the two-channel/terminal Kondo model at the Toulouse point as well as of a resonant level between two half-infinite Tomonaga--Luttinger liquids. We analyze the…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…