scholarly journals Global Behavior of the Fourth – Order Difference Equation

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Mehmet Emre Erdogan
Keyword(s):  
Difference Equation ◽  
Fourth Order ◽  
Global Behavior ◽  
Order Difference ◽  
Order Difference Equation

scholarly journals The global behavior of a quadratic difference equation

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6203-6210
Author(s):  
Vahidin Hadziabdic ◽  
Midhat Mehuljic ◽  
Jasmin Bektesevic ◽  
Naida Mujic
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Julia Set ◽  
Second Order ◽  
Global Behavior ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

In this paper we will present the Julia set and the global behavior of a quadratic second order difference equation of type xn+1 = axnxn-1 + ax2n-1 + bxn-1 where a > 0 and 0 ? b < 1 with non-negative initial conditions.

On the solutions of a higher order difference equation

2020 ◽  
Vol 27 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Raafat Abo-Zeid
Keyword(s):  
Difference Equation ◽  
Explicit Formula ◽  
Initial Conditions ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Forbidden Set ◽  
Order Difference Equation ◽  
The Difference

AbstractIn this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equationx_{n+1}=\frac{ax_{n}x_{n-k}}{bx_{n}-cx_{n-k-1}},\quad n=0,1,\ldots,where{a,b,c}are positive real numbers and the initial conditions{x_{-k-1},x_{-k},\ldots,x_{-1},x_{0}}are real numbers. We show that when{a=b=c}, the behavior of the solutions depends on whetherkis even or odd.

scholarly journals QUALITATIVE ANALYSIS OF A FOURTH ORDER DIFFERENCE EQUATION

2020 ◽  
Vol 10 (4) ◽  
pp. 1343-1354
Author(s):  
H. S. Alayachi ◽  
◽  
M. S. M. Noorani ◽  
E. M. Elsayed ◽  
◽  
...  
Keyword(s):  
Difference Equation ◽  
Qualitative Analysis ◽  
Fourth Order ◽  
Order Difference ◽  
Order Difference Equation
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