Pseudospectral discretization of nonlinear delay equations: new prospects for numerical bifurcation analysis

We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability and bifurcation of equilibria of the original model by available software packages for continuation and bifurcation for ordinary differential equations. Theoretical and numerical results confirm the effectiveness and the versatility of the approach, opening a new perspective for the bifurcation analysis of delay equations, in particular coupled renewal and delay differential equations.