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

Chen, Guanrong; Tian, Chuanjun; Shi, Yuming

Chaos Solitons Fractals 25, No. 3, 637-647 (2005).

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)

Keywords:

chaos in the sense of Devaney; stable system; 2-D discrete systems

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