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Closed Form Solution of a Symmetric Competitive System of Rational Difference Equations

Author(s): Tarek F. Ibrahim

Journal: Studies in Mathematical Sciences
ISSN 1923-8444

Volume: 5;
Issue: 1;
Start page: 49;
Date: 2012;
Original page

Keywords: Difference equation | Solutions | Convergence | Periodicity | Competitive

In this paper, we will study a symmetric competitive three-dimensional system of difference equations in the form:$$ x_{n+1} = frac {x_n}{z_n y_n}~ & ~y_{n+1} = frac {y_n}{x_n z_n}~ & ~z_{n+1} = frac {z_n}{y_n x_n}eqno{(1)} $$ where the initial values $x_0$, $y_0$, and $z_0$ are nonzero real numbers. Moreover, we have studied periodicity of solutions for this system. Finally we will give some numerical examples as applications.

Tango Rapperswil
Tango Rapperswil

RPA Switzerland

Robotic Process Automation Switzerland