Study of Stability of Non-linear Model with Hyperbolic Secant Function
JOURNAL OF EDUCATION AND SCIENCE,
2019, Volume 28, Issue 1, Pages 106-120
AbstractWe study a new definition of a non-linear model of time series with hyperbolic secant function in a discrete time. The suggested model consist of two parts the first part is (linear) and the second part is (non-linear) which contains the hyperbolic secant function. We approximate this model to be linear by using the local linearization technique. We find the non-zero unique singular point that satisfies the non-linear variation equation, also stability of the non-zero unique singular point and the limit cycle if it exists of the suggested model.
 Brockwell, P. J. and Davis, R. A.," Introduction of time series and forecasting".2nd Ed. Springer-Verlag , New York, Int., U.S.A. . (2002).
 Ozaki, T., "Non-linear phenomena and time series model". Invited paper, 43-rd Session of International Statistical Institute, Bulletin of the International Statistical Institute 49, Buenos Aires, Argentina. (1981).
 Mohammad A.A. and Salim A.J. ,"Stability of analysis of logistic autoregressive model". Qatar university, Sci. J. ,27,pp 17-28. (2007).
 Shi, Z., Tamura, Y., and Ozaki, T. ,"A Study on real-time detecting of machine tool chatter*". International Journal of The Japan Society for Precision Engineering,Vol.32,No.3,pp 178-182. (1998).
 Priestley M.B., "Non-linear and non-stationary time series analysis". Academic Press Limited, 24-28 Oval Road, London NW1 7DX, Great Britain. (1988).
- Article View: 45
- PDF Download: 75