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 SIMULTECH. Madrid, Spain. (Accepted)

[img] PDF - Accepted Version
Restricted to SRO admin only

Download (11MB)

Abstract

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: 24 May 2017 11:16
URI: http://sro.sussex.ac.uk/id/eprint/68154

View download statistics for this item

📧 Request an update
Project NameSussex Project NumberFunderFunder Ref
Lyapunov Methods and Stochastic StabilityUnsetICELANDIC RESEARCH FUND152429-051