Introducing a Probabilistic Structure on Sequential Dynamical Systems, Simulation and Reduction of Probabilistic Sequential Networks

Details Introducing a Probabilistic Structure on Sequential Dynamical Systems, Simulation and Reduction of Probabilistic Sequential Networks Introducing a Probabilistic Structure on Sequential Dynamical Systems, Simulation and Reduction of Probabilistic Sequential Networks

2007-06-29

arxiv.org/abs/0707.0026v2

Biology

Quantitative Biology

Genomics

14 pages

Scientific paper

A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions. It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either an epimorphism or a monomorphism. Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given.

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