## Stability and chaos in 2-D discrete systems.(English)Zbl 1071.37018

Summary: This paper is concerned with 2-D discrete systems of the form $$x_{m+1,n}= f(x_{m,n},x_{m,n+1})$$, where $$f: \mathbb{R}^2\to \mathbb{R}$$ is a function and $$m,n\in\mathbb{N}_0= \{0,1,2,\dots\}$$. Some sufficient conditions for this system to be stable and a verification of this system to be chaotic in the sense of Devaney, respectively, are derived.

### MSC:

 37C75 Stability theory for smooth dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 39A11 Stability of difference equations (MSC2000)
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### References:

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