File(s) under permanent embargo
Complete Lyapunov functions: computation and applications
chapter
posted on 2023-06-10, 04:04 authored by Carlos Argáez, Peter GieslPeter Giesl, Sigurdur HafsteinMany phenomena in disciplines such as engineering, physics and biology can be represented as dynamical systems given by ordinary differential equations (ODEs). For their analysis as well as for modelling purposes it is desirable to obtain a complete description of a dynamical system. Complete Lyapunov functions, or quasi-potentials, describe the dynamical behaviour without solving the ODE for many initial conditions. In this paper, we use mesh-free numerical approximation to compute a complete Lyapunov function and to determine the chain-recurrent set, containing the attractors and repellers of the system. We use a homogeneous evaluation grid for the iterative construction, and thus improve a previous method. Finally, we apply our methodology to several examples, including one to compute an epigenetic landscape, modelling a bistable network of two genes. This illustrates the capability of our method to solve interdisciplinary problems.
History
Publication status
- Published
File Version
- Accepted version
Journal
Advances in Intelligent Systems and ComputingISSN
2194-5357Publisher
Springer International PublishingExternal DOI
Volume
873Page range
200-221Event type
conferenceBook title
Simulation and Modeling Methodologies, Technologies and ApplicationsISBN
9783030014698Series
Advances in Intelligent Systems and ComputingDepartment affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2022-06-24First Compliant Deposit (FCD) Date
2022-06-24Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC