Abstract
In this paper, we explore local stability, attractor, periodicity character, and boundedness solutions of the second-order nonlinear difference equation. Finally, obtained results are verified numerically.
Highlights
The qualitative analysis of difference equations has been steadily increasing. is is due to the fact that difference equations appear as mathematical models in statistical problems, queuing theory, combinatorial analysis, electrical networks, genetics in biology, probability theory, economics, psychology, stochastic time series, sociology, geometry, number theory, etc
Berenhaut and Stevic [4] have explored the behaviour of the following difference equation: xn+1
Motivated from aforementioned studies, we explore the behavior of the following difference equation: xn+1 an + xxpnpn− 1, n 0, 1, . . . , (6)
Summary
The qualitative analysis of difference equations has been steadily increasing. is is due to the fact that difference equations appear as mathematical models in statistical problems, queuing theory, combinatorial analysis, electrical networks, genetics in biology, probability theory, economics, psychology, stochastic time series, sociology, geometry, number theory, etc. Positive solution of (8) is bounded and persists if 0 < p < 1. By eorem 2.6.2 of [14], y∗ is a global attractor for all positive solutions of (20), and it is bounded. Let the positive solution of (8) is xn∞ n − 1.
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