Analysing dynamical systems towards computing complete Lyapunov functions

Argáez, Carlos, Giesl, Peter and Hafstein, Sigurdur (2017) Analysing dynamical systems towards computing complete Lyapunov functions. SIMULTECH 2017, Madrid, Spain, 26/07/17 - 28/07/17. Published in: Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, 2017, Madrid, Spain. 134-144. Madrid, Spain. ISBN 9789897582653

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Ordinary differential equations arise in a variety of applications, including e.g. climate systems, and can exhibit complicated dynamical behaviour. Complete Lyapunov functions can capture this behaviour by dividing the phase space into the chain-recurrent set, determining the long-time behaviour, and the transient part, where solutions pass through. In this paper, we present an algorithm to construct complete Lyapunov functions. It is based on mesh-free numerical approximation and uses the failure of convergence in certain areas to determine the chain-recurrent set. The algorithm is applied to three examples and is able to determine attractors and repellers, including periodic orbits and homoclinic orbits.

Item Type: Conference Proceedings
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 24 May 2017 11:16
Last Modified: 18 Oct 2017 00:58

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Project NameSussex Project NumberFunderFunder Ref
Lyapunov Methods and Stochastic StabilityUnsetICELANDIC RESEARCH FUND152429-051