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

International audienceThe theoretical study of the stability of thenumerical solution of a differential system may be complicatedor even not feasible when the system is largeand nonlinear. Here it is shown that such a study canbe experimentally done by using stochastic arithmetic andits discrete approach known as the CESTAC method.The CESTAC method has been first proposed since morethan forty years by M. La Porte and J. Vignes as an experimentalstatistical method to estimate the accuracy on theresult of numerical program [10], [14]. Later an abstractformalization of the theory called Stochastic Arithmetichas been developed and many of its algebraic propertieshave been studied [2], [4], [5]. Here a brief presentationof stochastic arithmetic, of its main properties and ofthe different software existing for its implementation aregiven. Then it is demonstrated that the use of stochasticarithmetic in the solver of a differential system can easilyreveal whether the computed solution is stable or not.Moreover the stability can be studied with respect to thecoefficients of the system or with respect to the initialconditions. At the end it is also pointed out that the samemethod can be used to detect instabilities due to the usedsolver. Some examples taken from the biological literatureare given [1], [6], [7]