Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: Frequency domain method

• Published in: Applied mathematics and computation Vol. 216; no. 3; pp. 940 - 950
• Main Authors: Afuwape, Anthony Uyi, Castellanos, Jairo Eloy
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.04.2010; Elsevier
• Subjects: 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; 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
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2010.01.109

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.