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Persistence and permanence in mass-action models of biological interaction networks

The most common models for dynamics of biological interaction networks (such as the dynamics of concentrations in biochemical reaction networks, the spread of infectious diseases within a population, and population dynamics in an ecosystem) are given by mass-action dynamical systems. Persistence and permanence are properties of dynamical systems related with the existence of strictly positive lower bounds on coordinates of trajectories within the positive orthant. For example, they are important in understanding properties of biochemical networks (e.g., will a chemical reactant be available indefinitely in the future, or will it be completely consumed), and also in ecology (e.g., will a species become extinct in an ecosystem, or will it survive indefinitely), and in the dynamics of infectious diseases (e.g., will an infection die off, or will it infect the whole population). We formulate the Persistence Conjecture, which says that weakly reversible mass-action systems are persistent, independent of the values of parameters in the system. We prove this conjecture for two-species systems, even if reaction rates are allowed to vary in time. This allows us to also prove the three-dimenisonal Global Attractor Conjecture, which says that complex balanced systems have a global attractor in each linear invariant subspace. We also describe some applications to general polynomial dynamical systems and power-law systems.

Type of Seminar:
IfA Seminar
Prof. Gheorghe Craciun
Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison
Jul 05, 2011   13:30

ETL K25, Physikstrasse 3
Contact Person:

Heinz Koeppl
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