Displaying similar documents to “Solving a collection of free coexistence-like problems in stability”

Prolongations and stability in dynamical systems

J. Auslander, P. Seibert (1964)

Annales de l'institut Fourier

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Les auteurs étudient la notion de prolongement au sens de T. Ura et ses relations avec la notion d’ensembles positivement invariants. La stabilité au sens de Liapounoff est équivalente à l’invariance par prolongement. Les auteurs dégagent ensuite la notion de “prolongements abstraits” et les notions de stabilité correspondantes; la stabilité absolue (associée au prolongement minimal transitif) et la stabilité asymptotique jouent un rôle important.

On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point

Jiří Šremr (2025)

Applications of Mathematics

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We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations....

Stability of a class of adaptive nonlinear systems

Andrzej Dzielinski (2005)

International Journal of Applied Mathematics and Computer Science

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This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class...

Stability modulo singular sets

J. Iglesias, A. Portela, A. Rovella (2009)

Fundamenta Mathematicae

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A new concept of stability, closely related to that of structural stability, is introduced and applied to the study of C¹ endomorphisms with singularities. A map that is stable in this sense is conjugate to each perturbation that is equivalent to it in a geometric sense. It is shown that this kind of stability implies Axiom A and Ω-stability, and that every critical point is wandering. A partial converse is also shown, providing new examples of C³ structurally stable maps.