Related papers: A new approach in the theory of ordinary different…

A topological degree based averaging principle has been proposed by J. Mawhin in his PhD thesis [J. Mawhin, Le Probleme des Solutions Periodiques en Mecanique non Lineaire, These de doctorat en sciences, Universite de Liege, 1969]. In his…

In this paper we propose some continuation theorems for the periodic problem \begin{equation*} \begin{cases} \, x_{i}' = g_{i}(t,x_{i+1}), &i=1,\ldots,n-1, \\ \, x_{n}' = h(t,x_{1},\ldots,x_{n}), \\ \, x_{i}(0)=x_{i}(T), &i=1,\ldots,n,…

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…

The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…

Motivated by problems coming from different areas of the applied science we study the periodic solutions of the following differential system $$x'(t)=F_0(t,x)+\varepsilon F_1(t,x)+\varepsilon^2 R(t,x,\varepsilon),$$ when $F_0$, $F_1$, and…

By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…

Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…

We deal with a planar differential system of the form \begin{equation*} \begin{cases} \, u' = h(t,v), \\ \, v' = - \lambda a(t) g(u), \end{cases} \end{equation*} where $h$ is $T$-periodic in the first variable and strictly increasing in the…

Using Mawhin's coincidence degree theory, we obtain some new continuation theorems which are designed to have as a natural application the study of the periodic problem for cyclic feedback type systems. We also discuss some examples of…

In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an…

In this paper, we consider a class of nonautonomous multi-scale stochastic partial differential equations with fully local monotone coefficients. By introducing the evolution system of measures for time-inhomogeneous Markov semigroups, we…

In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…

Aim of this paper is to investigate the existence of periodic solutions of a nonlinear planar autonomous system having a limit cycle x_0 of least period T_0>0 when it is perturbed by a small parameter, T_1-periodic, perturbation. In the…

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…

We establish an averaging principle on the real semi-axis for semi-linear equation \begin{equation}\label{eqAb1} x'=\varepsilon (\mathcal A x+f(t)+F(t,x))\nonumber \end{equation} with unbounded closed linear operator $\mathcal A$ and…

Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of Brouwer degree theory. Between the…

Topological degree theory is a useful tool for studying systems of differential equations. In this work, a biological model is considered. Specifically, we prove the existence of positive T-periodic solutions of a system of delay…

We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic…

Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…