Open Access
Original Articles
Continuation of Periodic Orbits of a Third Order Oscillator under Autonomous Perturbation
Z. Afsharnejadafsharnejad@math.um.ac.irDepartment of MathematicsFaculty of Mathematical SciencesFerdowsi University of MashhadIranView full profile → , A. Golmakanigolmakani@math.um.ac.irDepartment of MathematicsFaculty of Mathematical SciencesFerdowsi University of MashhadIranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Jul 2006
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2006.10698518
- Pages:
- 191–197
Abstract
We consider systems of nonlinear third-order differential equations depending on a small parameter such that the unperturbed system has a three dimension manifold of periodic solutions. We impose some conditions on the system in order to reduce the third order perturbed system to the second one. By using Poincare-Andronov-Hopf theorem we prove the existence of many periodic solutions the perturbed system.
Keywords
References
- Afsharnejad, Z. and Golmakani, A.preprint
- Amster, P., De Napoli, P. and Mariani, M.C. “ Periodic Solutions of a Resonant Third-Order Equation ” . In To be appear in
- Friedrichs, K.O.1946 . “ On nonlinear vibrations of the third-order ” . In , Inst. Math. Mech 65 – 103 . New York University . in:
- Guckenheimer, J. and Holmes, P.1990 . “ Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ” . In , Vol. 42 , New York: Springer-Verlage .
- Hale, J.K. and Koçak, H.1991 . , Texts in Applied Mathematical Sciences Vol. 3 , New York: Springer-Verlage .
- Mehri, B. and Niksirat, M.2000 . The existence of periodic solutions for the non-linear third-order autonomous O.D.Es . , 5 : 163 – 171 .
- Perko, L.1991 . , Springer-Verlage .
- Rabiei Motlagh, O. and Afsharnejad, Z.2003–4 . Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations . , : 209 – 228 .
- Rabiei Motlagh, O. and Afsharnejad, Z.2003 . Existence of periodic solutions and Bonded Invariant Sets for Non-Autonomous Third-Order Differential Equations . , 31 ( 3 ) : 295 – 308 .
- Rabiei Motlagh, O., Esfahani, J.A. and Afsharnejad, Z.2004 . Existence of turbulent behavior for non-chaotic two dimensional jets . , 293 : 329 – 344 .
- Rauch, L.L.1950 . Oscillations of a third order nonlinear autonomous system, in: Contributions to the Theory of Nonlinear Oscillations . , 20 : 39 – 88 . in:
- Li, B.1981 . Uniqueness and stability of a limit cycle for a third-order dynamical system arising in neuron modeling . , 5 : 13 – 19 .
- Zhang, Z. and Wang, Z.2004 . Periodic solutions of the third order functional equations . , 292 : 115 – 134 .
Views: 57Downloads: 85Citations: 0
