Abstract
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results.
Highlights
It is very amusing to explore the nature of the solutions of a higher-order rational difference equation and to explain the local asymptotic stability of its equilibrium points. e inspection of some properties associated with these equations is a very enormous activity
Applications of discrete dynamical systems and difference equations have appeared recently in many fields of science and technology. ere is no doubt that the theory of difference equations will continue to play an important role in mathematics as a whole
It is very interesting to investigate the behavior of solutions of a system of nonlinear difference equations and to discuss the local asymptotic stability of their equilibrium points. ere are many papers in which systems and behavior of rational difference equations have been studied see [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
Summary
It is very amusing to explore the nature of the solutions of a higher-order rational difference equation and to explain the local asymptotic stability of its equilibrium points. e inspection of some properties associated with these equations is a very enormous activity. It is very amusing to explore the nature of the solutions of a higher-order rational difference equation and to explain the local asymptotic stability of its equilibrium points. Applications of discrete dynamical systems and difference equations have appeared recently in many fields of science and technology. It is very interesting to investigate the behavior of solutions of a system of nonlinear difference equations and to discuss the local asymptotic stability of their equilibrium points. Ere are many papers in which systems and behavior of rational difference equations have been studied see [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. We recall some basics and preliminaries that will be useful in our results and investigation
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