Dynamics under Geometric Dissipation
Petre Birtea, Dan Com\u{a}nescu
TL;DR
This paper establishes conditions under which adding geometric dissipation of gradient type stabilizes equilibrium points and periodic orbits in dynamical systems, and describes their domains of attraction.
Contribution
It provides new sufficient conditions for asymptotic stabilization using geometric dissipation and characterizes the domain of attraction for stable states.
Findings
Conditions for asymptotic stabilization established
Domain of attraction described for stable equilibria
Applicable to systems with geometric dissipation
Abstract
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of asymptotic stability.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Cosmology and Gravitation Theories