Stability and Spatial Chaos in 2D Hénon System

Authors

Fuyan Sun, College of Information Science and Engineering, Henan University of Technology, Zhengzhou, 450001, ChinaFollow
Zongwang Lü, College of Information Science and Engineering, Henan University of Technology, Zhengzhou, 450001, ChinaFollow

Author Country (or Countries)

China

Abstract

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,),

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100234

Recommended Citation

Sun, Fuyan and Lü, Zongwang (2016) "Stability and Spatial Chaos in 2D Hénon System," Applied Mathematics & Information Sciences: Vol. 10: Iss. 2, Article 34.
DOI: http://dx.doi.org/10.18576/amis/100234
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss2/34