Mapping resonance regions in loop networks with spatio-temporal-symmetry

The nonlinear dynamics of a network of n cells where the connections are periodically switched in a loop/ring configuration is analyzed. Each cell is a nonlinear dynamical system which may behave as an oscillator. As system parameters are changed, the forcing frequency of the switching law interacts with natural frequencies of the system giving rise to resonance phenomena. The resonance regions corresponding to different rotation numbers (Arnold tongues) are mapped in two parameter space through the use of two-parameter continuation technique. Moreover, as the forcing induce spatio-temporal symmetries in the system, each tongue divides regions with different symmetries of the multiperiodic regimes.