Global behavior of a three-dimensional system of difference equations of order three

Abstract

In this paper, we investigate the global behavior of the positive solutions of the system of difference equations

u_{n+1}=((α₁u_{n-1})/(β₁+γ₁v_{n-2}^{p})), v_{n+1}=((α₂v_{n-1})/(β₂+γ₂w_{n-2}^{q})), w_{n+1}=((α₃w_{n-1})/(β₃+γ₃u_{n-2}^{r}))

for n∈ℕ₀ where the initial conditions u_{-i},v_{-i},w_{-i} (i=0,1,2) are non-negative real numbers and the parameters  α_{j},β_{j},γ_{j} (j=1,2,3) and p,q,r are positive real numbers, by extending some results in the literature.

Keywords

• System of difference equations,stability,global behavior,periodic solution

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