Abstract
Delay-induced oscillations are widely observed in biological systems such as gene regulation and neural activities. Synchronization among delay-induced oscillations plays important roles in physiology. Therefore, it is significant to establish a method to analyze synchronization properties of delay-induced oscillations. Phase reduction is a mathematical method to analyze such synchronization phenomena. Recently, phase reduction was extended to analyze mathematical models of delay-induced oscillations. However, derivation of synchronization properties of an experimental delay-induced oscillation from phase reduction of its mathematical model has yet to be demonstrated. Here, we demonstrated the validity of a method to derive synchronization properties of a delay-induced oscillation from phase reduction. We generated a delay-induced oscillation experimentally by an electrical circuit. We derived phase response curve and synchronization conditions with periodic external forces by two methods: phase reduction and electrical experiment. We compared the results of the two methods, then phase response curves and synchronization conditions were generally consistent between the two methods. In conclusion, the validity of a method to derive synchronization properties of a delay-induced oscillation from phase reduction was indicated.
