Oscillation and stability of nonlinear discrete models exhibiting the Allee effect

Mathematica Slovaca

E. Elabbasy¹  H. El-Metwally¹  S. Saker¹ 

关键词: oscillation;    stability;    discrete population model;   

DOI  :  10.2478/s12175-007-0020-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, we consider the discrete nonlinear delay population model exhibiting the Allee effect (*)$$x_{n + 1} = x_n exp left( {a + bx_{n - au }^p - cx_{n - au }^q } ight),$$ where a, b and c are constants and p, q and Ï„ are positive integers. First, we study the local stability of the equilibrium points. Next, we establish some oscillation results of nonlinear delay difference equations with positive and negative coefficients and apply them to investigate the oscillatory character of all positive solutions of equation (*) about the positive steady state x * and prove that every nonoscillatory solution tends to x *.

【 授权许可】

Unknown