This post is from Dr John Bissell, a physicist researching
tipping points in mathematical systems for the project. In a
conference that had largely focused on `tipping points’ in human
society, especially those involving the spread of `buzzwords’,
`innovation’ and `trends’, Prof Richard Law‘s talk on ecological
dynamics (for those who might not have a clue as to what
ecological dynamics means this rather humorous rap might help)
acted as an important reminder of the role `tipping points’
might play in natural systems. Perhaps the most classic–if not
defining–example of a `tipping point’ is the fold bifurcation,
and Law began his discussion here. Broadly speaking, fold
bifurcations occur when changes in a system’s underlying
parameters alter the number of its steady-states (solutions to
the system that stay constant over time), for example, if the
prevailing steady-state is destroyed, then the whole system may
need to rapidly reconfigure to a new and often quite different
equilibrium. These kinds of catastroph