[PDF] Top 20 Global dynamics of some systems of higher order rational difference equations

... difference equations and systems is a topic of great ...dynamical systems and difference equations have appeared recently in many areas such as ecology, population dynamics, queuing ... See full document

... of systems () was proposed in all its generality by Camouzis et ...the global behavior of solu- tions to all systems () whose maps are bounded and thus provide answers to many of the open problems ... See full document

... and global behavior of the unique positive equilibrium point, and rate of convergence of positive solutions of systems () and () which converge to its unique positive equilibrium ...difference ... See full document

... competitive systems in the plane, when one of the eigenvalues of the linearized system at an equilibrium hyperbolic or non-hyperbolic is by absolute value smaller than 1 while the other has an arbitrary ... See full document

... Although difference equations are sometimes very simple in their forms ,they are extremely difficult to understand thoroughly the behavior of their solutions ...studied global behavior of nonlinear ... See full document

... Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete and as such these equations are in their own ... See full document

... nonlinear rational difference equations of a higher order is quite challenging and rewarding, and the results about these equations offer prototypes towards the development of ... See full document

... dynamical systems is becoming very popular as it comes naturally in various biological sys- tems including many other applied disciplines ...dynamical systems and difference equations ... See full document

... Recently, rational difference equations have attracted the attention of many researchers for various ...nonlinear equations which are, in some cases, treatable but their dynamics present ... See full document

... a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common ...the global and local properties of the ... See full document

... dynamical systems and difference equations developed greatly dur- ing the last twenty-five years of the twentieth ...difference equations also experienced enormous growth in many ...ical systems ... See full document

... of Difference Equations has been growing ...that difference equations appear as mathematical models describing real life situations in probability theory, queuing theory, statistical problems, ... See full document

... whose dynamics differ significantly from other equations in this ...of dynamics of the class of equations ...are some cases that have resisted a complete ... See full document

... For some difference equations, although their forms (or expressions) look very simple, it is extremely difficult to understand thoroughly the global behaviors of their ... See full document

... Methods and ideas by de Moivre were later developed by Euler ([3]). The study was continued by Lagrange (see, e.g., [4, 5]), Laplace (see, e.g., [6]), and many other scientists. Several methods for solving some ... See full document

... di¤erence equations or discrete dynamical systems are a fertile research area, not only in mathematics but also in many applied science such as economics, ...di¤erence equations or discrete dynamic ... See full document

... Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential ... See full document

... Some properties of algebraic difference equations of first order Liu Advances in Difference Equations (2017) 2017 334 DOI 10 1186/s13662 017 1395 8 R E S E A R C H Open Access Some properties of algeb[.] ... See full document

... For the second-order equation 1.1 , we have the following theorem which provides new information about the decreasing fast solutions obtained by Aprahamian et al. 1. Theorem 1.4. Adopt the hypotheses of Theorem ... See full document

... We also establish a linearized oscillation theorem accordin to which, when m is odd, every solution of Eq.1 oscillates if and only if every solution of an associated linear equation.. os[r] ... See full document