Two typical steady-state bifurcations for time-reversible vector field families

Abstract

Two typical steady-state bifurcations for time-reversible vector field families are studied, including allowance for a nontrivial nullspace forced by time-reversal symmetry. Under certain nondegeneracy conditions, it is shown that either a nontime-symmetric pitchfork or a time-symmetric transcritical bifurcation occurs. The method is extended to the equivariant case and applied by way of example to a class of time-reversible problems with D n × O(2) symmetries which includes the particle sedimentation model known as the Stokeslet model. © 2001 Plenum Publishing Corporation.