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

P.E. Kloeden

doi:10.3934/cpaa.2004.3.161

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2004, Volume 3, Issue 2: 161-173. Doi: 10.3934/cpaa.2004.3.161

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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: February 28, 2003

Revised: November 30, 2003

Published: May 2004

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Abstract

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.

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Mathematics Subject Classification: 34C23, 34C27, 37G10.

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