Speaker
Description
We consider systems of delay differential equations (DDEs) with discrete delays, where the right-hand side is linear or a polynomial of low degree. Physical parameters are replaced by random variables to model and quantify uncertainties. Thus the solutions represent random processes. We expand a random process into the generalised polynomial chaos, which is a series consisting of orthogonal basis polynomials and unknown time-dependent coefficient functions. A stochastic Galerkin method yields a larger deterministic system of DDEs, whose solution represents an approximation of the coefficient functions. We investigate the properties of the stochastic Galerkin systems. In particular, the stability of stationary solutions is examined, where the associated characteristic equations typically yield an infinite set of eigenvalues. Bifurcation analysis can also be considered with respect to the delay as parameter. We present results of numerical computations using DDEs of epidemiological models as test examples.
