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In this paper we study the stability of one of a non linear autoregressive model with trigonometric term by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude that the proposed model under certain conditions have a non-zero singular point which is a asymptotically salable ( when 0 ) and have an orbitaly stable limit cycle . Also we give some examples in order to explain the method.
Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.
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