Flux through a Markov chain. (December 2016)

• Record Type: Journal Article
• Authors: Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel
• Is Part Of: Chaos, solitons and fractals. Volume 93(2016)
• Page Start: 136
• Page End: 146
• Publication Date: 2016-12
• Subjects: 40.03 dynamical systems -- Open stochastic dynamical systems -- 20.03 applications to other physics disciplines -- 50.02 biological networks; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.10.006
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The flux through a Markov chain of a conserved quantity (mass) is studied. Mass is supplied by an external source and ends in the absorbing states of the chain. Meaningful for modeling open systems whose dynamics has a Markov property. The analytical expression of mass distribution is given for a constant source. The expression of mass distribution is given for periodic or random sources. Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.