Related papers: On a second-order rational difference equation and…
We establish the boundedness character of solutions of a system of rational difference equations with a variable coefficient
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
We study kth order systems of two rational difference equations $$x_n=\frac{\alpha+\sum^{k}_{i=1}\beta_{i}x_{n-i} + \sum^{k}_{i=1}\gamma_{i}y_{n-i}}{A+\sum^{k}_{j=1}B_{j}x_{n-j} + \sum^{k}_{j=1}C_{j}y_{n-j}},\quad n\in\mathbb{N},$$…
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…
Recently, mathematicians have been interested in studying the theory of discrete dynamical system, specifically difference equation, such that considerable works about discussing the behavior properties of its solutions (boundedness and…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{\alpha + z_{n-1}}{\beta z_n + z_{n-1}}}$ with the real parameter $\alpha$, $\beta$ and arbitrary non-negative real initial conditions is investigated…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…
The dynamics of the second order rational difference equation in the title with complex parameters and arbitrary complex initial conditions is investigated. Two associated difference equations are also studied. The solutions in the complex…
The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…