Qualitative study of a second order difference equation

被引:11
作者
Berkal, Messaoud [1 ]
Navarro, Juan Francisco [1 ]
机构
[1] Univ Alicante, Dept Appl Math, Alicante, Spain
关键词
Difference equations; Neimark-Sacker bifurcation; stability; BIFURCATION; BEHAVIORS; STABILITY; MODELS;
D O I
10.55730/1300-0098.3375
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.
引用
收藏
页码:516 / 527
页数:13
相关论文
共 21 条
[1]  
Aloqeili M, 2007, J APPL MATHE COMPUT, V25, P375, DOI 10.1007/BF02832362
[2]   Qualitative behavior of a two-dimensional discrete-time prey-predator model [J].
Berkal, Messaoud ;
Navarro, Juan F. .
COMPUTATIONAL AND MATHEMATICAL METHODS, 2021, 3 (06)
[3]   Stability of a certain class of a host-parasitoid models with a spatial refuge effect [J].
Beso, E. ;
Kalabusic, S. ;
Mujic, N. ;
Pilav, E. .
JOURNAL OF BIOLOGICAL DYNAMICS, 2020, 14 (01) :1-31
[4]   Global analysis of solutions of xn+1 = βxn+δxn-2/A+Bxn+Cxn-1 [J].
Camouzis, E .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 316 (02) :616-627
[5]   On the recursive sequence Xn+1 = p+Xn-k/Xn [J].
DeVault, R ;
Kent, C ;
Kosmala, W .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2003, 9 (08) :721-730
[6]  
Din, 2018, INT J DYN CONTROL, V6, P778, DOI [10.1007/s40435-017-0341-7, DOI 10.1007/S40435-017-0341-7]
[7]   Neimark-Sacker bifurcation of a third-order rational difference equation [J].
He, Zhimin ;
Qiu, Jia .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (09) :1513-1522
[8]   Flip and Neimark-Sacker bifurcation in a differential equation with piecewise constant arguments model [J].
Kartal, S. .
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2017, 23 (04) :763-778
[9]  
Kocic V. L., 1993, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications
[10]   Global Asymptotic Stability and Naimark-Sacker Bifurcation of Certain Mix Monotone Difference Equation [J].
Kulenovic, M. R. S. ;
Moranjkic, S. ;
Nurkanovic, M. ;
Nurkanovic, Z. .
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2018, 2018