Related papers: On two and three periodic Lyness difference equati…
We consider the stochastically perturbed cubic difference equation with variable coefficients \[ x_{n+1}=x_n(1-h_nx_n^2)+\rho_{n+1}\xi_{n+1}, \quad n\in \mathbb N,\quad x_0\in \mathbb R. \] Here $(\xi_n)_{n\in \mathbb N}$ is a sequence of…
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We…
A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in…
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 investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
Simple form scalar differential equation with delay and non-linear negative periodic feedback is considered. The existence of slowly oscillating periodic solutions with the same period as the feedback coefficient is shown numerically within…
We study the discrete-time, real valued bounded process $\{X_n, n\in {\mathbb N} \}$ defined by a second order recurrence relation $X_{n+2} = \varphi(X_n,X_{n+1})$. We obtain the decay of correlations under analytical hypotheses on $\varphi…
In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…
We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Li\'enard type oscillators exhibit this interesting property. We show that a…
The goal of our work is to investigate the oscillation and asymptotic properties of a class of difference equations with a condition. In contrast to most previous studies, the oscillation of the investigated equation is obtained with only…
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 solution form of the system of nonlinear difference equations \begin{equation*} x_{n+1} = \frac{x_{n-k+1}^{p}y_{n}}{a y_{n-k}^{p}+b y_{n}},\ y_{n+1} = \frac{y_{n-k+1}^{p}x_{n}}{\alpha x_{n-k}^{p}+\beta x_{n}}, \quad n, p \in…
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent…
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…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
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…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…