Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance
نویسندگان
چکیده
One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately, and are well located.
منابع مشابه
Resonant Homoclinic Bifurcations with Orbit Flips and Inclination Flips
Homoclinic bifurcation with one orbit flip, two inclination flips and resonance in the tangent directions of homoclinic orbit is considered. By studying the associated successor functions constructed from a local active coordinate system, we prove the existence of double 1-periodic orbit, 1-homoclinic orbit, and also some coexistence conditions of 1-periodic orbit and 1-homoclinic orbit.
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تاریخ انتشار 2013