Parameter identification in periodic delay differential equations with distributed delay

In this study, a parameter identification approach for identifying the parameters of a periodic delayed system with distributed delay is introduced based on time series analysis and spectral element analysis. Using this approach the parameters of the distributed delayed system can be identified from the time series of the response of the system. The experimental or numerical data of the response is examined with Floquet theory and time series analysis techniques to estimate a reduced order dynamics, or truncated state space to identify the Floquet multipliers. Parameter identification is then completed using a dynamic map developed for the assumed model of the system which can relate the Floquet multipliers to the unknown parameters in the model. The parameter identification technique is validated numerically for first and second order delay differential equations with distributed delay.

► A method for parameter identification in periodic distributed delay systems is proposed.
► This approach estimates the parameters of the system from the response time series.
► An assumed model is discretized into a dynamic map using spectral element analysis.
► A reduced order dynamic is estimated from time series using proper orthogonal decomposition.
► The technique is validated numerically for 1st and 2nd order periodic distributed-delay systems.