| Abstract: |
| Oscillatory dynamics induced by time delay are frequently observed in natural and artificial systems. However, analytical frameworks for delay induced oscillations are not fully developed.
Here, we propose a framework of model reduction by using the Floquet theorem for general delay-differential equations (DDEs) exhibiting limit-cycle oscillations.
Especially, we illustrate that the adjoint eigenfunction corresponding to the Floquet zero eigenvalue provides analytical insights of synchronization properties. We further propose a practical numerical method to derive the adjoint eigenfunction. By using this function, original DDEs can be reduced to a simple phase equation without time-delay. We then demonstrate that the analyses of the phase equations provide analytical insights into synchronization properties of biological systems modelled by DDEs. |
|