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- W3137927706 abstract "<p style='text-indent:20px;'>In this work, we study the behavior of the solutions of following three-dimensional system of difference equations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> $ begin{equation*} x_{n+1} = f(y_{n}, y_{n-1}), , y_{n+1} = g(z_{n}, z_{n-1}), , z_{n+1} = h(x_{n}, x_{n-1}) end{equation*} $ </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=M1>$ nin mathbb{N}_{0} $</tex-math></inline-formula>, the initial values <inline-formula><tex-math id=M2>$ x_{-1} $</tex-math></inline-formula>, <inline-formula><tex-math id=M3>$ x_{0} $</tex-math></inline-formula>, <inline-formula><tex-math id=M4>$ y_{-1} $</tex-math></inline-formula>, <inline-formula><tex-math id=M5>$ y_{0} $</tex-math></inline-formula> <inline-formula><tex-math id=M6>$ z_{-1} $</tex-math></inline-formula>, <inline-formula><tex-math id=M7>$ z_{0} $</tex-math></inline-formula> are positive real numbers, the functions <inline-formula><tex-math id=M8>$ f, , g, , h:, left(0, +inftyright)^{2}rightarrowleft(0, +inftyright) $</tex-math></inline-formula> are continuous and homogeneous of degree zero. By proving some general convergence theorems, we have established conditions for the global stability of the corresponding unique equilibrium point. We give necessary and sufficient conditions on existence of prime period two solutions of the above mentioned system. Also, we prove a result on oscillatory solutions. As applications of the obtained results, some particular systems of difference equations defined by homogeneous functions of degree zero are investigated. Our results generalize some existing ones in the literature.</p>" @default.
- W3137927706 created "2021-03-29" @default.
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- W3137927706 date "2021-01-01" @default.
- W3137927706 modified "2023-10-18" @default.
- W3137927706 title "On a general homogeneous three-dimensional system of difference equations" @default.
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- W3137927706 doi "https://doi.org/10.3934/era.2021017" @default.
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