Impact of the updating scheme on stationary states of networks
Radicchi, F, Ahn, YY, Meyer-Ortmanns, HJ. Phys. A: Math. Theor. 41, 224010 (2008)
Abstract
From Boolean networks it is well known that the number of attractors as
a function of the system size depends on the updating scheme which is
chosen either synchronously or asynchronously. In this contribution, we
report on a systematic interpolation between synchronous and
asynchronous updating in a one-dimensional chain of Ising spins. The
stationary state for fully synchronous updating is antiferromagnetic.
The interpolation allows us to locate a phase transition between phases
with an absorbing and a fluctuating stationary state. The associated
universality class is that of parity conservation. We also report on a
more recent study of asynchronous updates applied to the yeast
cell-cycle network. Compared to the synchronous update, the basin of
attraction of the largest attractor considerably shrinks and the
convergence to the biological pathway slows down and is less dominant.
Both examples illustrate how sensitively the stationary states and the
properties of attractors can depend on the updating mode of the
algorithm.