Self-sustained oscillations in excitable tree networks

Many practical systems, such as heart and neural systems, are described by excitable media or networks. Various oscillations of coupled excitable units are typical system states, determining some important functions in realistic processes. Excitable units do not oscillate individually, while oscillations of coupled excitable cells can appear after the self-organizations of collective motions via mutual interactions. Therefore, different mechanisms underlying oscillations turn to be very crucial issues under investigation. So far, all mechanisms of the oscillations of excitable networks rely, with no exception, on the existence of the oscillation sources formed by successive excited units on loops. Here, we explore a novel oscillation mechanism in diffusively coupled excitable networks where loop existence is no longer required, and oscillations can be sustained due to the excitation propagations between two hubs linked by a chain of low-degree nodes. Some necessary conditions for the sustained oscillations on hub size, chain length and coupling strength are analyzed in detail. And the possible application and significance of the explored mechanism for realistic oscillations of practical excitable networks are briefly discussed.