From 7dad4922d7239edf3a4e403e94859a5cb3bb6a8e Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Mon, 2 Dec 2024 13:01:37 -0500 Subject: [PATCH] vault backup: 2024-12-02 13:01:37 --- .../2024-12-02 Delay Differential Equation.md | 8 ++++++++ 1 file changed, 8 insertions(+) create mode 100644 300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-12-02 Delay Differential Equation.md 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 000000000..18b10d1a9 --- /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 $t=0$ +