New Burst-Oscillation Mode in Paced One-Dimensional Excitable Systems

A new type of (BOM) is reported for the first time, by extensively investigating the response dynamics of a one-dimensional (1D) paced excitable system with unidirectional coupling. The BOM state is an alternating transition between two distinct phases, i.e., the phase with multiple short spikes and the phase with a long interval. The realizable region and the unrealizable region for the evolution of BOM are identified, which is determined by the initial pulse number in the system. It is revealed that, in the realizable region, the initial inhomogeneous BOM will eventually evolve to the homogeneously distributed (SOM), while it can maintain in the unrealizable region. Furthermore, several dynamical features of BOM and SOM are theoretically predicted and have been verified in numerical simulations. The mechanisms of the emergence of BOM are discussed in detail. It is revealed that three key factors, i.e., the linking time, the system length, and the local dynamics, can effectively modulate the pattern of BOM. Moreover, the suitable parameter region of the external pacing ( ) that can produce the new type of BOM, has been explicitly revealed. These results may facilitate a deeper understanding of bursts in nature and will have a useful impact in related fields.