Asymptotic behavior of nonlinear difference equations with delays

Asymptotic Behavior of Solutions of Nonlinear Difference Equations

The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) =∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...

Asymptotic Stability of Nonlinear Control Systems Described by Difference Equations with Multiple Delays

Abstract. In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Hölder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are i...

Asymptotic Behavior of some Rational Difference Equations

In this difference equation, Stability, Periodicity, boundedness, global Stability. We investigate some qualitative behavior of the solutions of the difference equation

Asymptotic behavior of a system of two difference equations of exponential form

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions