Multiple Nonlinear Oscillations in a 𝔻 3 × 𝔻 3 -Symmetrical Coupled System of Identical Cells with Delays

Abstract

A coupled system of nine identical cells with delays and ${𝔻}_3\times {𝔻}_3$-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.