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June  2004, 3(2): 161-173. doi: 10.3934/cpaa.2004.3.161

Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient

P.E. Kloeden 1,

1. 

FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.

Received  March 2003 Revised  December 2003 Published  March 2004

The zero solution of a vector valued differential equation with an autonomous linear part and a homogeneous nonlinearity multiplied by an almost periodic function is shown to undergo pitchfork or transcritical bifurcations to small nontrivial almost periodic soutions as a leading simple real eigenvalue of the linear part crosses the imaginary axis.
Keywords: Nonautonomous differential equation, almost periodic solutions, transcritical bifurcation., pitchfork bifurcation.
Mathematics Subject Classification: 34C23, 34C27, 37G10.
Citation: P.E. Kloeden. Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient. Communications on Pure and Applied Analysis, 2004, 3 (2) : 161-173. doi: 10.3934/cpaa.2004.3.161
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