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Periodic and nonperiodic solutions of the difference equation \(x_{n+1}=\max\{x_ n^ 2,A\}/x_ nx_{n-1}\). (English) Zbl 0890.39012

Elaydi, S. (ed.) et al., Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7–11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 9-17 (1997).
Summary: The periodic behaviour of the solution of the difference equation \[ x_{n+1}=\max\{x^2_n,A\}/x_nx_{n-1};\quad x_0,x_1,A\in(0,\infty) \] is investigated. It is shown that for \(A\) different from unity, the solution is not periodic for all values of \(x_0\), \(x_1\). In fact, it has a chaotic behaviour with strange attractors.
For the entire collection see [Zbl 0885.00051].

MSC:

39A12 Discrete version of topics in analysis
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
39A10 Additive difference equations
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