Capture the past to portray the future: Numerical bifurcation analysis of delay equations via pseudospectral methods
Via pseudospectral discretization, a nonlinear delay equation can be approximated with a system of ODEs, and its dynamical and bifurcation properties can be studied with existing software for ODEs. The pseudospectral discretization method can be applied to nonlinear integral and delay-differential equations, with discrete and distributed delays, finite and infinite delays, and some kinds of state-dependent delays.
I will present the method and illustrate its effectiveness with some examples from population dynamics and epidemiology.
