Methods Based on Polynomial Chaos for Quadratic Delay Differential Equations With Random Parameters

ABSTRACT We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos. We investigate the application of the stochastic Galerkin method and stochastic collocation techniques to compute unknown coefficient functions of the series. Furthermore, existence and local stability of stationary solutions are discussed for each type of method. We present results of numerical computations in two illustrative examples: a logistic equation and an epidemiological model.