Related papers: Phase and amplitude responses for delay equations …
This paper investigates a new class of equations called measure functional differential equations with state-dependent delays. We establish the existence and uniqueness of solutions and present a discussion concerning the appropriate phase…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
It is shown that the solution maps of an abstract functional differential equations (FDEs) are $\alpha$-contractions in the phase space equipped with an equivalent norm under appropriate assumptions. This result can be applied to…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…
Delay differential equations (DDEs) are widely used in mathematical modeling to describe physical and biological systems. Delays can impact model dynamics, resulting in oscillatory behavior. In physiological systems, this instability may…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
The method of harmonic balance (HB) is a spectrally accurate method used to obtain periodic steady state solutions to dynamical systems subjected to periodic perturbations. We adapt HB to solve for the stress response of the Giesekus model…
Surface waves on a liquid air interface excited by a vertical vibration of a fluid layer (Faraday waves) are employed to investigate the phase relaxation of ideally ordered patterns. By means of a combined frequency-amplitude modulation of…
Power electronic devices such as HVDC and FACTS can be used to improve the damping of poorly damped inter-area modes in large power systems. This involves the use of wide-area feedback signals, which are transmitted via communication…
We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to…
This paper integrates the damped harmonic oscillator into DSGE models to better capture delayed economic adjustments. By introducing a damping coefficient, I model economic recoveries as under-damped, critically damped, or over-damped…
This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be…
Since response lags are essential in the feedback loops and are required by most physical systems, it is more appropriate to stabilize McKean-Vlasov stochastic differential equations (MV-SDEs) with common noise through the implementation of…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.
A new time-delay estimation (TDE) technique based on dynamic programming is developed, to measures the time-varying time-delay between two signals. Dynamic programming based TDE technique provides a frequency response 5 to 10 times higher…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…