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A piecewise linear system of difference equations is one of the piecewise systems that has special characters like coexisting attracting sets. In this article, we also exhibit the coexisting attractors of 5-cycles and equilibrium point. We use some direct iterative calculations and an inductive statement to explain all behaviors of solutions belonging to the system with initial condition belonging to negative -axis. We also found intervals of initial conditions that solutions become 5-cycles and equilibrium point.
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