Numerical bifurcation analysis of cosymmetric dynamical systems

Gemici, Ömer Caner
In this thesis, bifurcation phenomena in dynamical systems with cosymmetry and Hamiltonian structure were investigated using numerical methods. Several numerical continuation methods and test functions for detecting bifurcations here presented. The numerical results for various examples are given using a numerical bifurcation analysis toolbox.


Solution of helmholtz type equations by differential quadrature method
Kuruş, Gülay; Tezer, Münevver; Department of Mathematics (2004)
This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
Implementation of the equivalence principle algorithm for potential integral equations
Farshkaran, Ali; Ergül, Özgür Salih; Department of Electrical and Electronics Engineering (2018)
In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalence principle algorithm (EPA) is described for solving arbitrary shaped perfect electric conductor (PEC) and penetrable objects. The main advantage of EPA is its efficiency thanks to the enhanced conditioning hence accelerated iterative solutions of the matrix equations derived from discretizations. For further enhancing the efficiency, the multilevel fast mult...
Conformal symmetry in field theory
Huyal, Ulaş; Tekin, Bayram; Department of Physics (2011)
In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.
Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids
Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007)
In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Elliptic curve pairing-based cryptography
Kırlar, Barış Bülent; Akyıldız, Ersan; Department of Cryptography (2010)
In this thesis, we explore the pairing-based cryptography on elliptic curves from the theoretical and implementation point of view. In this respect, we first study so-called pairing-friendly elliptic curves used in pairing-based cryptography. We classify these curves according to their construction methods and study them in details. Inspired of the work of Koblitz and Menezes, we study the elliptic curves in the form $y^{2}=x^{3}-c$ over the prime field $\F_{q}$ and compute explicitly the number of points $...
Citation Formats
Ö. C. Gemici, “Numerical bifurcation analysis of cosymmetric dynamical systems,” M.S. - Master of Science, Middle East Technical University, 2003.