Stability Analysis and Periodictly Properties of a Class of Rational Difference Equations

Abstract

The goal of this study is to investigate the global, local, and boundedness of the recursive sequenceT_{η+1}=r+((p₁T_{η-l₁})/(T_{η-m₁}))+((q₁T_{η-m₁})/(T_{η-l₁}))+((p₂T_{η-l₂})/(T_{η-m2}))+((q₂T_{η-m₂})/(T_{η-l₂}))+...+((p_{s}T_{η-l_{s}})/(T_{η-m_{s}}))+((q_{s}T_{η-m_{s}})/(T_{η-l_{s}})),where the initial values T_{-l_{1,}},T_{-l₁₂},...T_{-l_{s,}}, T_{-m₁}, T_{-m₂}and T_{-m_{s}} are arbitrary positive real numbers. It also investigates periodic solutions for special case of above equations.

Keywords

• difference equations
• stability
• boundedness
• solution of difference equation.