相关论文: Relative equilibria and relative periodic solution…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
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…
In this paper, we study the relative controllability of linear difference equations with multiple delays in the state by using a suitable formula for the solutions of such systems in terms of their initial conditions, their control inputs,…
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems…
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…
We study the existence and multiplicity of periodic solutions for singular $\varphi$-laplacian equations with delay on time scales. We prove the existence of multiple solutions using topological methods based on the Leray-Schauder degree. A…
Existence and spatio-temporal symmetric patterns of periodic solutions to second order reversible equivariant non-autonomous periodic systems with multiple delays are studied under the Hartman-Nagumo growth conditions. The method is based…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
Delayed feedback laser dynamics is described by means of Lang-Kobayashi equation model. Since a lot of initial states asymptotically approach to periodic attractor in the phase space, only periodic steady-state regimes have been studied…
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…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
The partial case of the planar $N+1$ body problem, $N\ge2$, of the type of planetary system with satellites is studied. One of the bodies (the Sun) is assumed to be much heavier than the other bodies ("planets" and "satellites"), moreover…
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…