| Title | Stability and bifurcation of planar autonomous systems of ODE / by Adour Mikirdits Mikirditsian | Thesis |
| Name(s) | Mikirditsian, Adour Mikirdits (Main Author)
American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics (Related name)
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| Publication | 2009
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| Link(s) | Click for full-text
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| Physical Details | vii, 41 leaves; 30 cm.
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| Subjects | Differential equations--Qualitative theory
Bifurcation theory
Differential equations
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| Classmarks | T:005293
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| Notes | Dissertation: Thesis (M.S.)--American University of Beirut, Dept. of Mathematics, 2009.
Dissertation: Advisor : Dr. Friedemann Brock, Associate Professor , Mathematics
Member of Committee : Dr. Bassam Shayya ,Associate Professor , Mathematics
Member of Committee : Dr. Tamer Tlas, Visiting Assistant Professor , Mathematics.
Bib. & Index: Bibliography : leaf 41.
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| Abstract | We consider first-order autonomous planar systems of ODE's which depend on a parameter, x' = F(s, x). We are interested in the bifurcation from an equilibrium point and from periodic orbits.
In a first part we study the stability of steady-state solutions, using Liapunov's technique. Then we investigate the bifurcations of nonhyperbolic equilibria in the case where the linearized operator has one zero and one negative eigenvalue. The dynamics of such a planar system is determined from that of an appropriate scalar
ODE. Furthermore, we study the bifurcation in the case where the linearized operator has purely imaginary eigenvalues, and we analyse the appearance of small periodic orbits near the equilibrium (Hopf bifurcation).
In a second part, we study periodic orbits far away from equilibrium points. We present conditions for the presence and absence of such periodic orbits, and we investigate their stability and local bifurcations. A special consideration will be given to the case where F(s, x) is a quadratic polynomial in x.
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Category | | | Jafet Archives and Special Collections | Thesis | T:5293:c.1 | ASC-Binding | Building Use |
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