A new chaotic behavior of a general model of the Henon map

被引：6
作者：
El-Sayed, Ahmed M. A. [1 ]
El-Raheem, Zaki F. E. [2 ]
Salman, Sanaa M. [2 ]
机构：
[1] Univ Alexandria, Fac Sci, Dept Math, Alexandria, Egypt
[2] Univ Alexandria, Fac Educ, Alexandria, Egypt
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2014年
关键词：
retarded functional equation; Henon map; fixed points; existence; uniqueness; bifurcation; chaos; chaotic attractor; PREDATOR-PREY SYSTEM; DISCRETE;
D O I：
10.1186/1687-1847-2014-107
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we are concerned with a general form of the Henon map as a retarded functional equation. The existence of a unique solution is proved. The continuous dependence of the solution and the local stability of fixed points are investigated. Chaos, bifurcation and chaotic attractor of the resulting system are discussed. In addition, we compare our results with the discrete dynamical system of the Henon map.
引用
收藏
页数：14
相关论文
共 22 条
[1]  
[Anonymous], 2004, ELEMENTS APPL BIFURC
[2]   THE GENERALIZED TIME-DELAYED HENON MAP: BIFURCATIONS AND DYNAMICS [J].
Bilal, Shakir ;
Ramaswamy, Ramakrishna .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2013, 23 (03)
[3]  
Bohai NA, 2007, NONLINEAR OSCIL, V10, P169
[4]   Periodic solutions and stability for a singularly perturbed linear delay differential equation [J].
da Cruz, Jose H. ;
Taboas, Placido Z. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (06) :1657-1667
[5]  
El-Sayed A.M.A., 2013, MALAYA J MAT, V3, P14
[6]   Dynamic Properties of the Predator-Prey Discontinuous Dynamical System [J].
El-Sayed, Ahmed M. A. ;
Nasr, Mohamed E. .
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2012, 67 (1-2) :57-60
[7]  
El-Sayed AMA, 2012, ALEX J MATH, V3
[8]  
El-Sayed AMA, 2012, MALAYA J MAT, V1, P15
[9]  
El-Sayed AMA, 2012, AM ACAD SCH RES J, V2, P28
[10]  
El-Sayed AMA, 2012, J MATH, V1
123