Complete Lyapunov functions: computation and applications

Argáez, Carlos, Giesl, Peter and Hafstein, Sigurdur (2019) Complete Lyapunov functions: computation and applications. In: Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, 873 . Springer International Publishing, pp. 200-221. ISBN 9783030014698

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Abstract

Many 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.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 24 Jun 2022 08:15
Last Modified: 24 Jun 2022 08:15
URI: http://sro.sussex.ac.uk/id/eprint/106589

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