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Mathematical definition

Consider a differential equation

du

dt

= f(u,a),     u Î Rn,a Î R    f: Rn+1® Rn .
(33)

We are interested in an equilibrium curve, i.e. f(u,a)=0. The defining function is therefore:

F(x) = f(u,a) = 0
(34)

with x=(u,a) Î Rn+1. Denote by v Î Rn+1 the tangent vector to the equilibrium curve at x.