Interactions of Andronov-Hopf and Bogdanov-Takens Bifurcations
نویسنده
چکیده
A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z2 Z2 symmetry. The methodology is based on Arnold's ideas of versal deformations of matrices for the linear analysis, and Poincar e normal forms for the nonlinear analysis of the system. Bifurcation submanifolds of codimension one and two are identi ed in the parameter space. Many di erent classes of solutions are determined in the state space, including equilibria, limit cycles, invariant tori and the possibility of homoclinic chaos. As an application, a mechanism for energy transfer between two widely-spaced oscillation modes without strong resonance is identi ed.
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