Jain, Sanjay and Krishna, Sandeep (1998) Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model. In: Physical Review Letters, 81 (25). pp. 5684-5687.
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A model of s interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among them. The graph evolves via mutations of the least fit species. Starting from a sparse random graph, we find that an autocatalytic set inevitably appears and triggers a cascade of exponentially increasing connectivity until it spans the whole graph. The connectivity subsequently saturates in a statistical steady state. The time scales for the appearance of an autocatalytic set in the graph and its growth have a power law dependence on s and the catalytic probability. At the end of the growth period the network is highly nonrandom, being localized on an exponentially small region of graph space for large s.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to The American Physical Society.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Division of Physical & Mathematical Sciences > Physics
|Date Deposited:||25 Aug 2008|
|Last Modified:||19 Sep 2010 04:34|
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