There are many areas of research related to the empirical analysis of time series which support The Real Business Cycle Theory, but researchers have rarely explored the possibility that business cycle fluctuations have a nonlinear aspect and that is intrinsically a phenomenon without exogenous chocks. According to the theoretical exception of Keynesian endogenous cycle, cyclical movements are not due to the optimal adjustments of erratic displacements compared the equilibrium or deviations of working economy or of the impulses caused by external shocks or unpredictable events, but rather of vulnerable and fatal instability through which economy is oriented and of how endogenous fluctuations' evolution can affect nonlinear dynamics structures of time series. In this study, an econometric examination of the Tunisian industrial production cycle would prove the existence of endogenous fluctuations through a Hopf bifurcation if the control parameter transition undergoes a change. Also, clarify how bifurcation Theory and endogenous instability can explain how chaos is generated endogenously. The aim of our paper is to investigate the potential asymmetric effects of industrial dynamics. As a special case, we expand upon other works on this issue, by assessing the effect of structural changing processes in an asymmetric transition function on smooth transition autoregressive (STAR) specification that exhibits a limited cycle. But, in many given times, a deterministic dynamical system has a chaotic character that can affect predictability. While our study is based on recent fields of dynamical economy and econometrics' nonlinear processes, our results would concern of different empirical simulations about the endogenous business cycle. Specially, we analyze some aspects of nonlinear dynamics time series including chaos by controlling a parameter