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Stability and Spatial Chaos in 2D Hénon System |
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PP: 739-746 |
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doi:10.18576/amis/100234
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Author(s) |
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Fuyan Sun,
Zongwang Lü,
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Abstract |
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| This paper is concerned with two-dimensional(2-D) discrete system of the following form
xm+1,n +axm,n+1 = f (m, (1+a)xm,n,bxm−1,n),
where a,m,b is a real parameters.We investigate the fixed planes, stability of the fixed planes and spatial chaos behavior for this system.
A stability condition for the fixed plane is given, and it is proven analytically that for some parameter values the system has a transversal
homoclinic orbit, which is a verification of this system to be chaotic in the sense of Li-Yorke. These results extend the corresponding
results in the one-dimensional (1-D) H´enon system:
xm+1,n0 = f (m, xm,n0,bxm−1,n0 ),
where n0 is a fixed integer. These results also extend the corresponding results in the 2-D Logistic system:
xm+1,n +axm,n+1 = f (m, (1+a)xm,n,), |
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