Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: Frequency domain method
We use the frequency domain method to prove that the zero solution of certain third order nonlinear delayed differential equations is asymptotically stable, (when there is no forcing term). We also prove the existence of a bounded solution which is exponentially stable, (when there is a bounded forc...
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| Published in | Applied mathematics and computation Vol. 216; no. 3; pp. 940 - 950 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Amsterdam
Elsevier Inc
01.04.2010
Elsevier |
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| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2010.01.109 |
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| Abstract | We use the frequency domain method to prove that the zero solution of certain third order nonlinear delayed differential equations is asymptotically stable, (when there is no forcing term). We also prove the existence of a bounded solution which is exponentially stable, (when there is a bounded forcing term). The situation for which the non-linear term is delayed is also proved. |
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| AbstractList | We use the frequency domain method to prove that the zero solution of certain third order nonlinear delayed differential equations is asymptotically stable, (when there is no forcing term). We also prove the existence of a bounded solution which is exponentially stable, (when there is a bounded forcing term). The situation for which the non-linear term is delayed is also proved. 2000 Mathematics Subject Classification: 34C25; 34C27; 34D25; 34K20 We use the frequency domain method to prove that the zero solution of certain third order nonlinear delayed differential equations is asymptotically stable, (when there is no forcing term). We also prove the existence of a bounded solution which is exponentially stable, (when there is a bounded forcing term). The situation for which the non-linear term is delayed is also proved. |
| Author | Afuwape, Anthony Uyi Castellanos, Jairo Eloy |
| Author_xml | – sequence: 1 givenname: Anthony Uyi surname: Afuwape fullname: Afuwape, Anthony Uyi email: aafuwape@yahoo.co.uk – sequence: 2 givenname: Jairo Eloy surname: Castellanos fullname: Castellanos, Jairo Eloy email: jeloy@matematicas.udea.edu.co |
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| Cites_doi | 10.1016/S0893-9659(03)00063-6 10.1134/S0012266108040022 10.1016/0362-546X(86)90115-X 10.1016/j.amc.2007.11.037 10.4171/pm/1831 10.1016/j.cam.2005.04.034 10.1073/pnas.49.2.201 10.1016/j.chaos.2007.08.034 |
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| Keywords | 34C27 34D25 Asymptotic stability 34C25 Periodic solutions Frequency domain method Exponential stability 34K20 Third order delay differential equation Non linear equation Numerical analysis Third order equation Existence of solution Applied mathematics Periodic solution Numerical stability |
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| SubjectTerms | 34C25 34C27 34D25 34K20 Asymptotic properties Asymptotic stability Classification Differential equations Exact sciences and technology Exponential stability Frequency domain method Frequency domains Mathematical analysis Mathematical models Mathematics Nonlinearity Numerical analysis Numerical analysis. Scientific computation Periodic solutions Sciences and techniques of general use Stability Third order delay differential equation |
| Title | Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: Frequency domain method |
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