Impact of the updating scheme on stationary states of networks

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.