Global dynamics of $(1,2)-$ type systems of difference equations

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Authors :

Muhammad Naeem Qureshi 1 and Abdul Qadeer Khan 2 *

Author Address :

1,2 Department of Mathematics, University of Azad Jammu & Kashmir, Muzaffarabad 13100, Pakistan.

*Corresponding author.

Abstract :

We study the global dynamics of following $(1,2)-$ type systems of difference equations:
egin{equation*}
x_{n+1}=frac{eta y_{n-1}}{1+mu x_{n-2}^p}, y_{n+1}=frac{mu x_{n-1}}{1+eta y_{n-2}^p},
end{equation*}
egin{equation*}
x_{n+1}=frac{eta y_{n-1}}{1+mu y_{n-2}^p}, y_{n+1}=frac{mu x_{n-1}}{1+eta x_{n-2}^p},
end{equation*}
where $eta, mu, p $ and initial conditions $x_{l}, y_{l}, l=-2,-1,0$ are non-negative real numbers. Several numerical simulations are provided to support obtained results.

Keywords :

$(1,2)-$ type systems of difference equations; equilibrium point; stability; rate of convergence.

DOI :

10.26637/MJM0602/0018

Article Info :

Received : January 06, 2018; Accepted : March 20, 2018.

 

 

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