Equilibrium Solution on a Two-dimensional Piecewise Linear Map
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Abstract
In this paper we study a behavior of a piecewise linear map with specific initial condition in the second quadrant. We show that there is a unique equilibrium point of the map. We found regions of initial conditions that solutions become an equilibrium point. We separate the region into sub-regions and investigate behaviors of solutions in each sub-region by direct calculations. We use inductive statements to assert that solutions of the map in each region of initial conditions are an eventually equilibrium point without using stability theorem.
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