We study the planar and scalar reductions of the nonlinear Lindemann
mechanism of unimolecular decay. First, we establish that the origin, a
degenerate critical point, is globally asymptotically stable. Second, we prove
there is a unique scalar solution (the slow manifold) between the horizontal
and vertical isoclines. Third, we determine the concavity of all scalar
solutions in the nonnegative quadrant. Fourth, we establish that each scalar
solution is a centre manifold at the origin given by a Taylor series. Moreover,
we develop the leading-order behaviour of all planar solutions as time tends to
infinity. Finally, we determine the asymptotic behaviour of the slow manifold
at infinity by showing that it is a unique centre manifold for a fixed point at
infinity.Comment: 27 pages, 6 figure
