Computation of a contraction metric for a periodic orbit using meshfree collocation

Giesl, Peter (2019) Computation of a contraction metric for a periodic orbit using meshfree collocation. SIAM Journal on Applied Dynamical Systems, 18 (3). pp. 1536-1564. ISSN 1536-0040

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Abstract

Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. We consider a contraction metric, i.e. a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions in all directions perpendicular to the flow are contracted, then there exists a unique periodic orbit, which is exponentially stable. In this paper we propose a construction method using meshfree collocation to approximately solve a matrix-valued PDE problem. We derive error estimates and show that the approximation is itself a matrix-valued PDE problem. We derive error estimates and show that the approximation is itself a contraction metric if the collocation points are sufficiently dense. We apply the method to several examples.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 09 Jul 2019 08:40
Last Modified: 12 Sep 2019 14:15
URI: http://sro.sussex.ac.uk/id/eprint/84768

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