• Abdulghafoor Jasim Salim College of Computer Science and Mathematics University of Mosul
  • Kais Ismail Ebrahem College of Education for pure science University of Mosul
  • Suhirman Universitas Teknologi Yogyakarta
Keywords: Non-linear Autoregressive model, Limit cycle, singular point, Stability



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.


[1] M.B. Priestly (1988)” Nonlinear and Non-stationary Time series Analysis “, Academic Press.
[2] T. Subba Rao, (1981),” On the Theory of Bilinear Time Series Models”, Journal of Royal statistical society: series B.
[3] Ozaki, T., and Oda, H.,(1978)," Nonlinear Time Series Model Identification by Akaka's information Criterion, In information and System", ed. Dubuisson. Pergamon Press, Oxford
[4] Tong H. (2011), “Threshold models in time series analysis — 30 years on “, Statistics and Its Interface Volume 4 (2011) 107–118.
[5] Tong, H.,(1990)," Nonlinear Time Series., A dynamical System Approach, Oxford University Press, New york.
[6] Ozaki, T.(1985)," Nonlinear Time Series Models and Dynamical system", Handbook of statistic ,Vol. 5(ed. Hannan , E.,J. ,and Krishnailah, P., R.,and Rao,M. M.) Elsevier Science Publisher B.,V.,PP(25-83)
[7] Omid S. Fard (2007)” linearization and nonlinear stochastic differential equation with locally Lipchitz condition “, J. of applied mathematics, Vol.1, 2007, no. 52, 2553-2536.
[8] Ozaki, T.,(1982), " The Statistical Analysis of Perturbed Limit Cycle Process Using Nonlinear Time series Models", Journal of Time Series Analysis, Vol.3No.1,PP(29-41).
[9] Chatifield,C.,(2000)," Time series Forecasting ", Chapman and Hall, The University Of Bath, London, UK.
[10] Chatifield,C.,(2004) sixth edition," The Analysis of Time series : An introduction", Chapman and Hall, The University Of Bath, London, UK.
How to Cite
Abdulghafoor Jasim Salim, Ebrahem, K. I., & Suhirman. (2020). STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD. International Journal of Engineering Technology and Natural Sciences, 2(1), 27 - 31.