Applied Mathematics & Information Sciences

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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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