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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| Format: | Article |
| Language: | English |
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Tikrit University
2025-02-01
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| Series: | Tikrit Journal of Pure Science |
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| 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 |
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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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| format | Article |
| id | doaj-art-2ae032028ab3413dad4fda4db1d5596f |
| institution | OA Journals |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Tikrit University |
| record_format | Article |
| 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 AT azheramohammed thestabilityforlimitcycleoflomaxautoregressivemodel AT ruyakabbas stabilityforlimitcycleoflomaxautoregressivemodel AT azheramohammed stabilityforlimitcycleoflomaxautoregressivemodel |