diff --git a/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-12-02 Delay Differential Equation.md b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-12-02 Delay Differential Equation.md new file mode 100644 index 00000000..18b10d1a --- /dev/null +++ b/300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-12-02 Delay Differential Equation.md @@ -0,0 +1,8 @@ +$$ \frac{dx}{dt} = \vec f(x(t), x(t-\tau), x(t-\tau_2), ..., x(t-\tau_n)) $$ +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 $t=0$ +