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.


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


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