Related papers: Characteristic matrix functions for delay differen…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
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…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
In this note we consider local invariant manifolds of functional differential equations representing differential equations with state-dependent delay. Starting with a local center-stable and a local center-unstable manifold of the…
A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects the regularity of the (coefficients of the) linearized…
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…
We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between…
In the present paper, we consider a Cauchy problem for a linear second order in time abstract differential equation with pure delay. In the absence of delay, this problem, known as the harmonic oscillator, has a two-dimensional eigenspace…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…