In the last decades, the problem of stability of chaotic systems has generated a great deal of interest. In the early period of development, most of classical methods about the stability theory were concerned with deterministic dynamical systems and used the Lyapunov function method. Recently, classical methods have been extended to stochastic systems like flow induced vibrations (suspension bridge, tube bundles) or turbulent fluctuations. The use of stochastic methods lead to improve the knowledge about their stability. Several works have shown that the largest Lyapunov exponent could be used as an indicator of stochastic stability. In this paper, the effect of a random excitation (additive and multiplicative noise) on the stability of some dynamical systems will be analysed in using the Itô calculus. Some new expressions for the largest Lyapunov exponent are given and compared with numerical solutions.
F. JEDRZEJEWSKI, Institut National des Sciences et Techniques Nucléaires, CEA, Centre d'Etudes de Saclay, France