Related papers: Periodic Solutions in a Simple Delay Differential …
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
The issue of inheriting periodicity of an exact solution of a dynamic system by a difference scheme is considered. It is shown that some difference schemes (midpoint scheme, Kahan scheme) in some special cases provide approximate solutions…
For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The…
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…
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…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
In this paper it is dealt with the following system of difference equations x_{n+1}=((a_{n})/(x_{n}))+((b_{n})/(y_{n})), y_{n+1}=((c_{n})/(x_{n}))+((d_{n})/(y_{n})), n in N_0, where the initial values x_0,y_0 are positive real numbers and…
A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…
We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations.
We study stability of so-called synchronous slowly oscillating periodic solutions (SOPSs) for a system of identical delay differential equations (DDEs) with linear decay and nonlinear delayed negative feedback that are coupled through their…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
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…
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 establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
In this paper we prove that the following delay differential equation \[ \frac{d}{dt}x(t)=rx(t)\left(1-\int_{0}^{1}x(t-s)ds\right), \] has a periodic solution of period two for $r>\frac{\pi^{2}}{2}$ (when the steady state, $x=1$, is…