Abstract
In the present paper, the global attractor, local stability, and boundedness of the solution of sixth order difference equations are investigated analytically and numerically. The exact solutions of three equations are presented by utilizing Fibonacci sequence. We also analyse the periodicity of a sixth order difference equation. The considered difference equations are given by yn+1=Ayn−1±Byn−1yn−3/Cyn−3±Dyn−5, n=0,1,…, where the initial conditions y−5,y−4,y−3,y−2,y−1, and y0 are arbitrary real numbers and the values A,B,C, and D are defined as positive real numbers.
Highlights
The theory of difference equations has been studied by a huge number of researchers. is can be attributed to the importance of this field in modelling a large number of natural phenomena
Difference equations are used in modelling some real-life problems appeared in biology, physics, economy, engineering, etc
Difference equations become apparent in the study of discretization methods for differential equations
Summary
The theory of difference equations has been studied by a huge number of researchers. is can be attributed to the importance of this field in modelling a large number of natural phenomena. Almatrafi [2] obtained the exact solutions of the following systems of the difference equations: xn+1 yn− 1 xn− 1yn− 3 Alotaibi [5] analysed the global stability and examined the periodic solution of the following difference equation: yn+1 Cinar [10] investigated the solution of the difference equation: xn+1
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