Nonlinear Waves in a Two-ring Network with a Transverse Coupling

A two-ring network coupling by a transverse link is considered in this paper. Divide and conquer algorithm is used to analyze the stability and Hopf bifurcation values. Nonlinear waves (such as synchronization and reflection waves) are studied using the center manifold theorem and normal form theory. It is shown that appropriate settings of transverse coupling can guarantee the backup of the complicated dynamics from one ring to the other.