Catalan numbers out of a stochastic cellular automaton

2019 ◽  
Vol 60 (1) ◽  
pp. 012701
Author(s):  
Mariusz Białecki
Keyword(s):  
Cellular Automaton ◽  
Catalan Numbers ◽  
Stochastic Cellular Automaton

TRAIL FOLLOWING AND AGGREGATION OF MYXOBACTERIA

1995 ◽  
Vol 03 (04) ◽  
pp. 1059-1068 ◽  
Author(s):  
ANGELA STEVENS
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Cellular Automaton ◽  
Particle System ◽  
Jump Process ◽  
Trail Following ◽  
Starting Point ◽  
Chemotaxis System ◽  
Stochastic Cellular Automaton ◽  
Moderate Interaction

This paper deals with the question whether myxobacteria can aggregate due to slime trail following. The starting point is a stochastic cellular automaton model where the bacteria are particles moving due to the rules of a jump process. A simplified case of this automaton shows that the slime has to be produced in an extremely high amount to account for aggregation. This simplified cellular automaton is connected to a stochastic many particle system from which a system of partial differential equations can be derived, a so-called chemotaxis-system. Here a moderate interaction between the particles has to be taken into account. In the last part this system is analyzed numerically to see whether it reflects the results of the simplified cellular automaton.

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

2011 ◽  
Vol 32 (9) ◽  
pp. 1952-1961 ◽  
Author(s):  
Pieter Van der Weeën ◽  
Jan M. Baetens ◽  
Bernard De Baets
Keyword(s):  
Cellular Automaton ◽  
Chemical Reaction ◽  
Stochastic Cellular Automaton
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