Gröbner bazlarının lineer olmayan diferansiyel denklemlere bazı uygulamaları

In this thesis, we study various applications of the Groebner bases method to problems in nonlinear dynamical systems such as determining the existence and computing symbolically the jerky dynamics of given nonlinear dynamical systems, constructing Lyapunov functions, determining critical levels and investigating robustness problem with structure uncertainity of nonlinear dynamical systems. Numerical examples are given for illustration. All computations are performed by package Mathematica.