Computational approach - P Giesl 15.4.2018.pdf (543.82 kB)
Computational approach for complete Lyapunov functions
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posted on 2023-06-10, 04:04 authored by Carlos Argáez, Peter GieslPeter Giesl, Sigurdur Freyr HafsteinOrdinary differential equations arise in a variety of applications, including climate modeling, electronics, predator-prey modeling, etc., and they can exhibit highly complicated dynamical behaviour. Complete Lyapunov functions capture this behaviour by dividing the phase space into two disjoint sets: the chain-recurrent part and the transient part. If a complete Lyapunov function is known for a dynamical system the qualitative behaviour of the system’s solutions is transparent to a large degree. The computation of a complete Lyapunov function for a given system is, however, a very hard task. We present significant improvements of an algorithm recently suggested by the authors to compute complete Lyapunov functions. Previously this methodology was incapable to fully detect chain-recurrent sets in dynamical systems with high differences in speed. In the new approach we replace the system under consideration with another one having the same solution trajectories but such that they are traversed at a more uniform speed. The qualitative properties of the new system such as attractors and repellers are the same as for the original one. This approach gives a better approximation to the chain-recurrent set of the system under study.
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Publication status
- Published
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- Accepted version
Journal
Springer Proceedings in Mathematics and StatisticsISSN
2194-1009Publisher
Springer International PublishingExternal DOI
Volume
248Page range
1-11Event type
conferenceBook title
Dynamical Systems in Theoretical PerspectiveISBN
9783319965970Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2022-06-24First Open Access (FOA) Date
2022-06-24First Compliant Deposit (FCD) Date
2022-06-24Usage metrics
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