Global Dynamics of Certain Mix Monotone Difference Equation

Mathematics

Senada Kalabušić¹  Mehmed Nurkanović²  Zehra Nurkanović² 

[1] Department of Mathematics, University of Sarajevo, 71000 Sarajevo, Bosnia and Herzegovina;Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia and Herzegovina;

关键词: difference equations;    equilibrium;    period-two solutions;    period-four solutions;    global stability;    monotonicity;   

DOI  :  10.3390/math6010010

来源: DOAJ

【 摘 要 】

We investigate global dynamics of the following second order rational difference equationxn + 1 =x n xn − 1 + αx n+ βxn − 1 ax n xn − 1 + bxn − 1 , where the parameters α , β ,a ,b are positive real numbers and initial conditions x− 1and x 0 are arbitrary positive real numbers. The map associated to the right-hand side of this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the corresponding parametric space. In most cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.

【 授权许可】

Unknown