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

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 μ 1 6 due to resonance, rather than the expected rate of μ 1 2 . This phenomenon provides an enhancement algorithm for low contrast images.