Abstract
Recently, we have proposed a generalized theory of the synchronization of rhythms based on the concept of biological receptors. The theory can achieve both mutual synchronization and external synchronization. However, previous work has neglected the particular case of the external control of a group of mutually coupled oscillators. In nature, we often encounter complex systems that consist of many subsystems, e.g., organs that consist of many cells. However, without proper control, it is likely for an external field to break the synchronous behavior of subsystems. In this study, we generalize the biological receptor scheme such that external synchronization can be achieved without breaking the mutual synchronization of coupled oscillators. Furthermore, in the original receptor scheme, the frequency of the synchronized state is different from that of individual oscillators. This frequency difference is a major drawback from theory to technological applications. This drawback of the receptor model can be solved using an external field properly. Because receptors are ubiquitous in cells, we hope that this work will promote further understanding of the control mechanism of complex biological systems.
