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Les systèmes dynamiques discrets
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TLDR
In this paper, the authors describe a systeme dynamique discret, which is an ensemble of elements, prenant chacun un nombre fini d'etats, and evoluant, dans un temps discret par interactions mutuelles.Abstract:
Un systeme dynamique discret est un ensemble fini d'elements, prenant chacun un nombre fini d'etats, et evoluant, dans un temps discret, par interactions mutuelles. Ce livre est consacre a l'analyse de la dynamique temporelle de tels systemes. Grace a des outils de metrique discrete, on etablit des resultats de convergence globale (contraction booleenne) convergence locale vers un point fixe ou vers un cycle, et ceci pour differents modes operatoires."read more
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Theoretical advances in artificial immune systems
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Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework
TL;DR: The existence of a positive circuit in G(x) for some x is a necessary condition for the existence of several fixed points in the dynamics, and it is shown that theexistence of a negative circuit is anecessary condition forthe existence of an attractive cycle.
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Scalar equations for synchronous Boolean networks with biological applications
TL;DR: The scalar equation approach to Boolean network models is further developed and then applied to two interesting biological models and gives immediate information about both cycle and transient structure of the network.
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Necessary conditions for multistationarity in discrete dynamical systems
Adrien Richard,Jean-Paul Comet +1 more
TL;DR: This work generalizes the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R.R. Thomas used in the course of his analysis of genetic networks, gets a more general variant of R. Thomas' conjecture.
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Negative circuits and sustained oscillations in asynchronous automata networks
TL;DR: In this article, it was shown that the presence of a negative feedback circuit in the interaction graph of a dynamical system is a necessary condition for the system to produce sustained oscillations.