Resonant bifurcation of feed-forward chains and application in image contrast enhancement

Abstract

This paper discusses the 1:1 resonant Hopf bifurcations and nilpotent singularity of non-semisimple for feed-forward chains with delay. The analytical formulas show that at synchrony-breaking bifurcation points the center manifold inherits a feed-forward structure. Using this structure, an analytical formula of normal form is derived to provide that near the points of 1:1 resonant Hopf bifurcation the amplitude of periodic solutions grows at the surprising rate of μ16 due to resonance, rather than the expected rate of μ12. This phenomenon provides an enhancement algorithm for low contrast images.