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Scientific Bulletin of Namangan State University

Abstract

In the article we consider the systems of differential equations ̇ , that depend on a set of parameters μ. For example, the vector field for the pendulum nominally depends upon two parameters: its length and the strength of gravity. Our goal is to investigate what happens to the flow of the system when parameters vary slightly. Do the properties of the orbits just change slightly, or can orbits be destroyed, created, or otherwise changed dramatically? A bifurcation occurs when there is dramatic change in the dynamics.

First Page

20

Last Page

26

References

1. A.A.Andronov, E.A.Leontovich, I.I.Gordon, A.G.Mayer, Teoriya bifurkatsiy dinamicheskix sistem na ploskosti, «Nauka», Moskva. 1967. 2. L.Perko, Differential equations and dynamical sistems, Springer 2000 3. A.N.Kolmogorov, S.B.Fomin, Elementы teorii funksiy i funksionalnogo analiza, Moskva, «Nauka». 1989.

Erratum

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