The mechanism of rotating waves in a ring of unidirectionally coupled Lorenz systems (Q2208182)

Coupled systems with unidirectional ring links are special systems with cyclic group symmetry. They can exhibit periodic solutions in the form of rotating waves. In this paper, the authors study the bifurcation of rotating waves in a ring of unidirectional coupled Lorenz systems. They establish the Hopf bifurcation theorem of rotating-periodic solutions in general odd-dimensional systems or systems coupled by multiple odd-dimensional subsystems. Numerical simulation verifies the correctness of the theoretical results.