Periodic Solution of a Piecewise Linear System of Difference Equations with Initial Condition in Positive X - Axis
Abstract
In this paper, we study a piecewise linear system of difference equations with initial condition in positive x-axis which remains an open problem. We find that there exist 5-cycles and equilibrium point. We use some direct iterative calculations and mathematical induction to prove the behaviors of solutions of the system. We separate positive x-axis into subintervals and investigate the behaviors of solutions in each of subintervals. We also find that for such initial condition the attractors are only 5-cycles and equilibrium point. Moreover, we reveal the boundary of basins of attractions for 5-cycles and equilibrium point.
Keywords : piecewise linear system ; periodic solution ; equilibrium point ; difference equation
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