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Article Dans Une Revue Computer Modeling in Engineering and Sciences Année : 2010

Absolute Stability of Chaotic Asynchronous Multi-Interactions Schemes for Solving ODE

Résumé

Multi Interaction Systems, used in the context of Virtual Reality, are dedicated to real-time interactive simulations. They open the way to the in virtuo experimentation, especially useful in the domain of biochemical kinetics. To this purpose, chaotic and asynchronous scheduling of autonomous processes is based upon desynchronization of phenomena involved in the system. It permits inter- activity, especially the capability to add or remove phenomena in the course of a simulation. It provides methods of resolution of ordinary differential systems and partial derivative equations. Proofs of convergence for these methods have been es- tablished, but the problem of absolute stability, although it is crucial when consid- ering multiscale or stiff problems, has not yet been treated. The aim of this article is to present absolute stability conditions for chaotic and asynchronous schemes. We give criteria so as to predict instability thresholds, and study in details the sig- nificant example of a damped spring-mass system. Our results, which make use of random matrices products theory, stress the point that the desynchronization of phenomena, and a random scheduling of their activations, can lead to instability.
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Dates et versions

hal-00861381 , version 1 (22-10-2013)

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  • HAL Id : hal-00861381 , version 1

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Pascal Redou, Laurent Gaubert, Gireg Desmeulles, Vincent Rodin, Pierre-Antoine Béal, et al.. Absolute Stability of Chaotic Asynchronous Multi-Interactions Schemes for Solving ODE. Computer Modeling in Engineering and Sciences, 2010, 70 (1), pp.11-40. ⟨hal-00861381⟩
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