Bogdanov- Takens Bifurcation
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In bifurcation theory, a field within mathematics, a Bogdanov-Takens bifurcation is a well-studied example of a bifurcation with co-dimension two, meaning that two parameters must be varied for the bifurcation to occur. It is named after Rifkat Bogdanov and Floris Takens, who independently and simultaneously described this bifurcation. A system y'' = f(y) undergoes a Bogdanov-Takens bifurcation if it has a fixed point and the linearization of f around that point has a...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In bifurcation theory, a field within mathematics, a Bogdanov-Takens bifurcation is a well-studied example of a bifurcation with co-dimension two, meaning that two parameters must be varied for the bifurcation to occur. It is named after Rifkat Bogdanov and Floris Takens, who independently and simultaneously described this bifurcation. A system y'' = f(y) undergoes a Bogdanov-Takens bifurcation if it has a fixed point and the linearization of f around that point has a double eigenvalue at zero (assuming that some technical nondegeneracy conditions are satisfied).
