Reaksiyon difüzyon denkleminin bifürkasyonu

First of all, we review important topological properties of elliptic curves in dependence of coeffi cient of de fining equation of elliptic curves. Especially, we study singular points of elliptic curves by means of discriminant of defi ning equa- tion of the curve. We see that the elliptic curve is non singular if it is de fined by an equation whose coe fficients will give non zero discriminant. In Chapter 2, we review fundamental properties of elliptic functions, i.e. doubly periodic meromorphic functions on projective space P1(C). In Chapter 3, we de fine Jacobi elliptic functions as inverse function to elliptic in- tegrals. Moreover, we see that Jacobi elliptic function solves mechanic problem on the periodicity of Galileo pendulum. In Chapter 4, we study solution to non linear reaction diff usion equation. This equa- tion is described by an quartic polynomial that depends on three parameters. We examine the bifurcation of the elliptic curves associated to this quartic equation. That is to say first we draw a bifurcation diagram in a 2-dimensional parameter space for a fixed energy level parameter. Then we shall achieve case studies for each connected component of the bifurcation diagram to analyze the behavior (e.g. the length of the period) of periodic solution to the reaction di usion equation expressed by Jacobi elliptic function. Keywords: Elliptic curves, singular, non singular points, discriminant, doubly pe- riodic, meromorphic, projective space, Jacobi elliptic function,reaction di ffusion equation.