Acta Biotheoretica

, Volume 62, Issue 3, pp 243–284 | Cite as

Stability, Complexity and Robustness in Population Dynamics

Regular Article

Abstract

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks.

Keywords

Structural stability Liapunov stability Asymptotic stability Attractors Genetic networks Network robustness 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.AGIM, FRE CNRS 3405, Faculty of Medicine of GrenobleUniversity J. FourierLa TroncheFrance
  2. 2.LIRIMA-UMMISCO, Faculté des SciencesUniversité de YaoundéYaoundéCameroun

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