Related papers: Delay differential equations with periodic coeffic…
We have demonstrated that a rather weak external optical feedback with delay can lead to the mode switching of the counterpropogating modes. The delay time should be longer then any system characteristic time. The equations describing the…
In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…
The time-periodic scalar delay differential equation $\dot x(t)=\gamma f(t,x(t-1))$ is considered, which leads to a resonant bifurcation of the equilibrium at critical values of the parameter. Using Floquet theory, spectral projection and…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear delayed feedback terms are perturbed by a pair of standard…
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
When studying a general system of delay differential equation with a single constant delay, we encounter a certain lack of uniqueness in determining the coefficient of one of the third order terms of the series defining the center manifold.…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on an associated submanifold of the Banach space $C^1([-h,0],\mathbb{R}^n)$. We extend a recent result on…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.
We study the dynamics of the positive solutions of a second-order, Ricker-type exponential difference equation with periodic parameters. We find that qualitatively different dynamics occur depending on whether the period p of the main…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
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…
In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
We propose here a stochastic binary element whose transition rate depends on its state at a fixed interval in the past. With this delayed stochastic transition this is one of the simplest dynamical models under the influence of ``noise''…
Due to simplicity and strong stability guarantees, predictor feedback methods have stood as a popular approach for time delay systems since the 1950s. For time-varying delays, however, implementation requires computing a prediction horizon…