Stochastic Arithmetic as a Tool to Study the Stability of Biological Models


  • Rene Alt* Pierre et Marie Curie University
  • Jean-Luc Lamotte Pierre et Marie Curie University



Stochastic arithmetic has been introduced since more than forty years byВ M. La Porte and Jean Vignes.В It has been first proposed as an experimental statistical method called the CESTAC method to estimate the accuracy on the result of numerical program.В An abstract formalization of the theory called Stochastic Arithmetic has been developed and many ofВ its algebraic properties have been studied.В Here a brief presentation of stochastic arithmetic, of it's main properties and of the different software existing for it's implementation are given.В Then it is shown that stochastic arithmetic can be easily used to experimentally study the stability of many differential systems proposed as models for biological processes.The stability can be studied with respect to the coefficients of the model or withВ respect to the initial conditions. Some examples based on the Monod equation are taken from the literature are. In the end it is also shown that the same method can be used to detect instabilities due toВ used the solver.

Author Biography

Jean-Luc Lamotte, Pierre et Marie Curie University







Conference Contributions