Given a system of ODEs,
du
dt | = f(u,a), u Î Rn,a Î R f: Rn+1® Rn . (1) |
an equilibrium curve is a one-dimensional manifold endowed with coordinates (u,a) defined by
F(x) = f(u,a) = 0, (2)
where F: Rn+1® Rn are the defining functions. The Jacobian matrix of (2) involved in the continuation has the form
Fx = [ fu(u,a) | fa(u,a) ] (4)
No special properties of this matrix are assumed and the generic lineair algebra library is used to solve appearing lineair system of equations.
Several test functions can be computed along the equilibrium curve to detect and process equilibrium singularities.
An equilibrium curve can be continued from a user-supplied point, an equilibrium point (including limit point and Hopf point) or a branching point on the computed equilibrium curve. To continue of the equilibrium curve, one needs to set relevant parameters to start from
a point
an equilibrium
a branching point
via the Starter window.