Obsidian/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-12-02 Delay Differential Equation.md

\frac{dx}{dt} = \vec f(x(t), x(t-\tau), x(t-\tau_2), ..., x(t-\tau_n))

Example: First order DE

\frac{dx}{ct} = -x \rightarrow x(t) = x_0e^{-t}

First order DDE:

\frac{dx}{dt} = -x(t-1)

This is a problem. We cannot use an initial value, we need an initial history function (IHF). This is the behaviour of x(t) defined in an interval [-\tau_0, 0], assuming solution time starts at t=0