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On nonautonomous discrete dynamical systems driven by means. (English) Zbl 1139.39303

Summary: We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): \(y_j(n+1)= F_j(n,{\mathbf y}(n))\); \(j=1,\dots,k\), \(n=0,1,2,\dots\), where \({\mathbf y}(n)= (y_1(n),\dots,y_k(n))\in\mathbb R^k\), \({\mathbf y}(0)={\mathbf x}\), and \(F_j(n,\cdot)\) is a mean of \(k\) \((\geq 2)\) positive real numbers, that is, a real-valued function satisfying the internality property \(\min({\mathbf x})\leq F_j(n,{\mathbf x})\leq\max({\mathbf x})\).

MSC:

39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
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References:

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