Analyse
Les systèmes, optiquement bistables dans le régime stationnaire, peuvent présenter un régime chaotique caractérisé par une dimension de Lyapunov élevée. Cette dimension, calculée numériquement, est pratiquement égale au nombre de fois que le temps d’auto-corrélation de la force de réaction est contenu dans le retard. Cette loi qui s’interprète à l’aide d’une image très simple de la dynamique, devrait être valable pour tout processus à réaction retardée oscillante ou de courte portée et permettrait aux expérimentateurs d’estimer facilement la dimension des attracteurs chaotiques qu’ils sont susceptibles d’observer.
Abstract
Optical systems which display bistability in the station ary regime may exhibit high-dimensional chaos. The Lyapunov dimension of chaotic attractors is found to be almost equal to the delay time divided by the auto-correlation time of the feedback for two optical systems, the non linear ring cavity and the hybrid system, and for the Mackey-Glass model for white-cell production. This simple relationship will enable experimentalists to easily estimate the complexity of a high-dimension system.
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LE Berre, M., Ressayre, E. & Tallet, A. Chaos dans des systèmes optiques à réaction retardée. Ann. Telecommun. 42, 324–327 (1987). https://doi.org/10.1007/BF02995250
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DOI: https://doi.org/10.1007/BF02995250