Feed-forward networks, center manifolds, and forcing
The authors investigate the dynamics of a feed-forward network consisting of three cells in the vicinity of a Hopf bifurcation. By calculating the center manifold, they can show that the reduced bifurcation equations inherit the feed-forward structure from the original system and decouple into the normal form equations for a Hopf bifurcation and a periodically excited Duffing type equation close to primary resonance, where the excitation is introduced by the solution of the Hopf subsystem. The combined system has the remarkable feature that there is a branch of periodic solution, which grows like \(\lambda^{1/6}\).NEWLINENEWLINEIn the second part, the authors consider a resonant external excitation of their system and find an exciting variety of bifurcation diagrams: for certain combinations of parameters it is possible that several closed branches separate from the well-known shape of the bifurcation diagram of the Duffing equation.
scientific article; zbMATH DE number 6053022