The Stability for Limit Cycle of Lomax Autoregressive Model

In this research, we proposed a new non-linear model known as the Lomax autoregressive model, which is based on the cumulative distribution function of the Lomax distribution. Using the local linearization approximation technique, we found stability for the proposed first-order model's limit c...

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Main Authors: Ruya K. Abbas, Azher A. Mohammed
Format: Article
Language:English
Published: Tikrit University 2025-02-01
Series:Tikrit Journal of Pure Science
Subjects:
Online Access:https://tjpsj.org/index.php/tjps/article/view/1687
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author Ruya K. Abbas
Azher A. Mohammed
author_facet Ruya K. Abbas
Azher A. Mohammed
author_sort Ruya K. Abbas
collection DOAJ
description In this research, we proposed a new non-linear model known as the Lomax autoregressive model, which is based on the cumulative distribution function of the Lomax distribution. Using the local linearization approximation technique, we found stability for the proposed first-order model's limit cycle. Then, we generalized the conditions for the Lomax autoregressive model of order p and found stability for the limit cycle of period (q > 1). Some examples illustrate the state of stability, and we plot the trajectory for the model of different initial values.
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series Tikrit Journal of Pure Science
spelling doaj-art-2ae032028ab3413dad4fda4db1d5596f2025-08-20T02:36:23ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262025-02-0130110.25130/tjps.v30i1.1687The Stability for Limit Cycle of Lomax Autoregressive Model Ruya K. Abbas0Azher A. Mohammed1Department of Mathematics, College Science of Computer and Mathematics, Tikrit University, Tikrit, IraqDepartment of Mathematics, College Science of Computer and Mathematics, Tikrit University, Tikrit, Iraq In this research, we proposed a new non-linear model known as the Lomax autoregressive model, which is based on the cumulative distribution function of the Lomax distribution. Using the local linearization approximation technique, we found stability for the proposed first-order model's limit cycle. Then, we generalized the conditions for the Lomax autoregressive model of order p and found stability for the limit cycle of period (q > 1). Some examples illustrate the state of stability, and we plot the trajectory for the model of different initial values. https://tjpsj.org/index.php/tjps/article/view/1687Limit cycle Lomax autoregressive model Local linearization methodStability non-linear time series
spellingShingle Ruya K. Abbas
Azher A. Mohammed
The Stability for Limit Cycle of Lomax Autoregressive Model
Tikrit Journal of Pure Science
Limit cycle
Lomax autoregressive model
Local linearization method
Stability
non-linear time series
title The Stability for Limit Cycle of Lomax Autoregressive Model
title_full The Stability for Limit Cycle of Lomax Autoregressive Model
title_fullStr The Stability for Limit Cycle of Lomax Autoregressive Model
title_full_unstemmed The Stability for Limit Cycle of Lomax Autoregressive Model
title_short The Stability for Limit Cycle of Lomax Autoregressive Model
title_sort stability for limit cycle of lomax autoregressive model
topic Limit cycle
Lomax autoregressive model
Local linearization method
Stability
non-linear time series
url https://tjpsj.org/index.php/tjps/article/view/1687
work_keys_str_mv AT ruyakabbas thestabilityforlimitcycleoflomaxautoregressivemodel
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AT azheramohammed stabilityforlimitcycleoflomaxautoregressivemodel