Journal of innovative applied mathematics and computational sciences
Volume 3, Numéro 1, Pages 83-120
2023-06-30
On Dynamics And Solutions Expressions Of A System Of Three Dimensional Nonlinear Difference Equations
Authors : Al-rakhami Faiza . Elsayed E. .
Abstract
In this paper, we construct the solution expressions of fourth order nonlinear difference systems Φ_{n+1} =((Φ_{n-2}Ψ_{n-3})/(α+Ψ_{n}(±1±Γ_{n-1}Φ_{n-2}Ψ_{n-3}))), Ψ_{n+1} =((Ψ_{n-2}Γ_{n-3})/(δ+Γ_{n}(±1±Φ_{n-1}Ψ_{n-2}Γ_{n-3}))), Γ_{n+1} =((Γ_{n-2}Φ_{n-3})/(γ+Φ_{n}(±1±Ψ_{n-1}Γ_{n-2}Φ_{n-3}))), where α,δ and γ are arbitrary real numbers. Furthermore, the solution's qualitative behavior is explored, such as local stability and boundedness. In some cases, there are a periodic solutions. Finally, we provide numerical examples to support our conclusions.
Keywords
Rational difference equations ; solution of system of difference equation ; periodic solution ; recursive sequences ; local stability
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