Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems
This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t)=β0ωμp(t−τ)/(ωμ+pμ(t−τ))−γp(t) and it is shown that the exponential θ-method has the same order of convergence as...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/348384 |
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| _version_ | 1832563612418310144 |
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| author | Qi Wang Jiechang Wen |
| author_facet | Qi Wang Jiechang Wen |
| author_sort | Qi Wang |
| collection | DOAJ |
| description | This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t)=β0ωμp(t−τ)/(ωμ+pμ(t−τ))−γp(t) and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples. |
| format | Article |
| id | doaj-art-08c5b011510442e58ddeb73b1154f40d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-08c5b011510442e58ddeb73b1154f40d2025-02-03T01:13:02ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/348384348384Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control SystemsQi Wang0Jiechang Wen1School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, ChinaSchool of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, ChinaThis paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t)=β0ωμp(t−τ)/(ωμ+pμ(t−τ))−γp(t) and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.http://dx.doi.org/10.1155/2012/348384 |
| spellingShingle | Qi Wang Jiechang Wen Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems Journal of Applied Mathematics |
| title | Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems |
| title_full | Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems |
| title_fullStr | Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems |
| title_full_unstemmed | Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems |
| title_short | Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems |
| title_sort | numerical oscillations analysis for nonlinear delay differential equations in physiological control systems |
| url | http://dx.doi.org/10.1155/2012/348384 |
| work_keys_str_mv | AT qiwang numericaloscillationsanalysisfornonlineardelaydifferentialequationsinphysiologicalcontrolsystems AT jiechangwen numericaloscillationsanalysisfornonlineardelaydifferentialequationsinphysiologicalcontrolsystems |