  The concept of (auto)catalytic systems has become a cornerstone in
understanding evolutionary processes in various fields. The common ground is
the observation that for the production of new species/goods/ideas/elements
etc. the pre-existence of specific other elements is a necessary condition. In
previous work some of us showed that the dynamics of the catalytic network
equation can be understood in terms of topological recurrence relations paving
a path towards the analytic tractability of notoriously high dimensional
evolution equations. We apply this philosophy to studies in socio-physics,
bio-diversity and massive events of creation and destruction in technological
and biological networks. Cascading events, triggered by small exogenous
fluctuations, lead to dynamics strongly resembling the qualitative picture of
Schumpeterian economic evolution. Further we show that this new methodology
allows to mathematically treat a variant of the threshold voter-model of
opinion formation on networks. For fixed topology we find distinct phases of
mixed opinions and consensus.
