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Educational Programme
Final Grade
Year of Graduation
Alexander Apostolov
Determination of the Bifurcation Point of Dynamical System for Empirical Financial Series with Noise
Business Informatics
(Bachelor’s programme)
The primary purpose of this project is a research in the area of the bifurcation theory, it is necessary to understand how bifurcation points influence on the behavior of the dynamical systems where these bifurcations take place. In particular, bifurcations in the nonlinear systems with the weak noise impact were discussed here. As for real data sample, exchange rates of the USA dollar and the euro for the past several years were used in the project. Such kind of data is very comfortable for this type of the topic. The calculation system Wolfram Mathematica was used here for the mathematical implementation of the main project’s goals. There were many different variants but exactly this system was chosen because it provides a plenty of good opportunities of the data visualization.

As for further researches, it would be nice to continue to work out this topic later, while studying at the master’s degree educational program. The research’s results are supposed to be used in the bifurcation theory and the time series’ analysis.

This project consists of several parts:

1. The introduction with the definition of such important things as goals and the research’s object and subject;

2. The main body, which contains the detailed description of theoretical and practical aspects, the implementation of the main goal and its results’ interpretation;

3. The conclusion, where the project’s results are discussed and summarized;

4. The bibliography having the list of all used sources of the required information. The links are also given there.

A few words about the research’s modernity and relevance, it would be always relevant in econometrics, there are a lot of various ways of using such knowledge in stock markets or currency exchange markets and maybe in some other spheres of economics and science.

Keywords: nonlinear dynamics, dynamical system, bifurcation point, financial time series, noise

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