241 research outputs found
Connecting orbits in perturbed systems
No full textColonius F, Hüls T, Rasmussen M. Connecting orbits in perturbed systems. NONLINEAR DYNAMICS. 2010;59(4):569-578.We apply Newton's method and continuation techniques to determine heteroclinic connections in perturbed non-autonomous differential equations which do not exist for the underlying unperturbed system. This approach is particularly useful in a higher-dimensional context, where the numerical computation of invariant manifolds is very expensive. A detailed discussion of a four-dimensional model is presented, which describes a pendulum coupled to a harmonic oscillator
Decay rates for stabilization of linear continuous-time systems with random switching
No full textInternational audienceFor a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time
Controllability near a Hopf bifurcation
No full textControllability near a Hopf bifurcation / Fritz Colonius ; Gerhard Häckl ; Wolfgang Kliemann. - In: Conference on Decision and Control : Proceedings. - Tucson, Ar. : IEEE, 1992
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