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In this article our goal is to studying the stationary condition of EGARCH time series model which is proved by Nelson (1991) but what we did is to prove it with more simple and clearly defined method and this is done by using a dynamical approximation relying on local linearization method in the neighborhood of a non-zero singular point of EGARCH model. This method is being used to approximate a Nonlinear model to a linear autoregressive model. Beside that we found the orbitally stability condition of a limit cycle of EGARCH(1,1) model if the model possess it. Keywords: EGARCH, Local linearization method, Conditional variance, Limit cycle, Time series, Autoregressive model