9 lines
406 B
Markdown
9 lines
406 B
Markdown
$$ \frac{dx}{dt} = \vec f(x(t), x(t-\tau), x(t-\tau_2), ..., x(t-\tau_n)) $$
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Example:
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First order DE
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$$ \frac{dx}{ct} = -x \rightarrow x(t) = x_0e^{-t}$$
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First order DDE:
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$$\frac{dx}{dt} = -x(t-1)$$
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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 $t=0$
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