On The System of Rational Difference Equations \(x_{n}=f(x_{n-a₁},y_{n-b₁}),y_{n}=g(y_{n-b₂},z_{n-c₁}),z_{n}=h(z_{n-c₂},x_{n-a₂}) \)

Nihat Akgunes, Abdullah Selcuk Kurbanlı


In this paper we study the global behavior of positive solutions of the more general system of rational difference \(x_{n}=f(x_{n-a₁},y_{n-b₁}),  y_{n}=g(y_{n-b₂},z_{n-c₁}),  z_{n}=h(z_{n-c₂},x_{n-a₂}) \), where \(n∈ℕ, a₁,b₁,c₁,a₂,b₂,c₂∈{0,1,2,...}\) and the initial values \(x_{-a},x_{-a+1},...,x₀, y_{-b},y_{-b+1},...,y_{0,} z_{-c},z_{-c+1},...,z₀∈ℝ⁺\). We give sufficient conditions under which every positive solution of this system converges to the unique positive equilibrium


Behavior, Global behavior, Difference equations system


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