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Exponential stability in nonlinear difference equations. (English) Zbl 1055.39011

The authors consider the nonlinear difference equation of the form \[ x(n+1)=f(n,x(n)), n\geq 0, x(n_0)=x_0, n_0\geq 0 \] where \(x(n) \in\mathbb{R}^K, f(n,x(n)):Z^{+}\times R^K\rightarrow R^K\) is given nonlinear function satisfying \(f(n,0)=0\) for all \(n\in Z^{+}.\) By Lyapunov functional method a sufficient condition for the exponential stability of the zero solution of the above system is obtained.

MSC:

39A11 Stability of difference equations (MSC2000)
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