Mathematics Colloquium



Department of Mathematics
University of Nebraska at Omaha


WHEN:
Wednesday, March 9, 2005 at 2:30 PM

WHERE:
Durham Science Center, Room 255

WHAT:


Dora Matache

University of Nebraska at Omaha

Joint work with Jack Heidel, University of Nebraska at Omaha

will give a talk on

Random Boolean Networks governed by a generalization of the ECA Rule 126


ABSTRACT:
We consider a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, fixed or variable. The nodes, with randomly assigned neighborhoods, are updated based on various schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata (ECA). We provide formulae for the probability of finding a node in state 1 at a time t. We use simulation methods to generate consecutive states of the network for both the real systems and the models under the various updating schemes. The results match well. We study the dynamics of the models through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. The network behaviors range from order to chaos depending on the type of updating scheme used and the parameter combinations.


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