Abstract
In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.
Highlights
Difference equations are recognized as description of observed evolution of a phenomenon, where the majority of measurements of a time-evolving variable are discrete
Many results have been obtained in the theory of difference equations as more natural discrete analogues of corresponding results of differential equations
Difference equations have been widely used as mathematical models for describing real life situations in probability theory, queuing problems, stochastic time series, combinatorial analysis, statistical problems, number theory, geometry, electrical networks, quanta in radiation, economics, genetics in biology, psychology, sociology, refer [1,2,3,4,5,6,7,8]
Summary
Difference equations are recognized as description of observed evolution of a phenomenon, where the majority of measurements of a time-evolving variable are discrete As a result, these equations get their importance in arithmetical models. Many results have been obtained in the theory of difference equations as more natural discrete analogues of corresponding results of differential equations This could be true in case of the stability theory of Lyapunov. The applications of the differential equation theory are growing rapidly in a wide variety of fields (i.e., numerical analyses, finite mathematics, control theory, and computer science) This puts lots of potential on studying the difference equations theory in addition to the related disciplines. Rational difference equations have sparked the debate of many researchers They afford many examples of non-linear equations which are treatable, in many cases.
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