Dünaamiliste süsteemide ja geneetika mudelid

Abstract

Dynamic systems are systems, which develop or change in time. With every model in this thesis there is given a story about the origin of given system or equation and necessary information. In addition to models there are also different charts to simplify the understanding of the models. Systems in this thesis are based on differential equations, because differential equations describe dynamic systems, which are continuous in time. Attention is paid to systems, in which the differential equations are nonlinear, because these could lead to chaotic solutions. All the models are given with initial conditions and some models also have charts, which show the change of the solution if a parameter has been changed a little. It is clear, that all systems may not lead to chaos with every value, but if the parameters are changed and solutions are analysed, it is seen that even a slightest change may lead to a chaos. With models it is easy to experiment with the real world. Without such models we were often left to manipulate real systems in order to understand the relationships of cause and effect. Models help to realize the consequences of the actions of mankind without harming the nature or the real world. In this thesis, two basic genetic problems were discussed, the mating of two alleles and natural selection and mutation. These models are quite simple, yet they provide enough infor-mation to understand the base of these problems in the real world. It is also possible to make these models more precise, which will lead to more accurate results and more precise predictions to real life cause and effect situations. In conclusion, models just make a lot of things easier to understand.