Exponential Stability in Nonlinear Difference Equations
نویسندگان
چکیده
Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee exponential stability of the zero solution of a nonlinear discrete system. The theory is illustrated with several examples.
منابع مشابه
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+...
متن کاملSolving a nonlinear inverse system of Burgers equations
By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...
متن کاملSufficient conditions for the exponential stability of delay difference equations with linear parts defined by permutable matrices
This paper deals with the stability problem of nonlinear delay difference equations with linear parts defined by permutable matrices. Several criteria for exponential stability of systems with different types of nonlinearities are proved. Finally, a stability result for a model of population dynamics is proved by applying one of them.
متن کاملStability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...
متن کاملFuzzy difference equations of Volterra type
In this work we introduce the notion of fuzzy volterra dierence equations and study the dynamicalproperties of some classes of this type of equations. We prove some comparison theorems for theseequations in terms of ordinary volterra dierence equations. Using these results the stability of thefuzzy nonlinear volterra dierence equations is investigated.
متن کامل