Al-Saffar, A. and Kim, E. (2017) Sustainable theory of a logistic model - Fisher Information approach. Mathematical Biosciences, 285. pp. 81-91. ISSN 0025-5564
Abstract
Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher information has been evoked as a useful measure of sustainability and the variability of dynamical systems including self-organising systems. By utilising Fisher information, we investigate the sustainability of the logistic model for different perturbations in the positive and/or negative feedback. Specifically, we consider different oscillatory modulations in the parameters for positive and negative feedback and investigate their effect on the evolution of the system and Probability Density Functions (PDFs). Depending on the relative time scale of the perturbation to the response time of the system (the linear growth rate), we demonstrate the maintenance of the initial condition for a long time, manifested by a broad bimodal PDF. We present the analysis of Fisher information in different cases and elucidate its implications for the sustainability of population dynamics. We also show that a purely oscillatory growth rate can lead to a finite amplitude solution while self-organisation of these systems can break down with an exponentially growing solution due to the periodic fluctuations in negative feedback.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier. This is an author produced version of a paper subsequently published in Mathematical Biosciences. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Nonlinear system; Sustainability; Fisher Information; Driving parameters; Probability Density Function(PDF) |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 10 Jan 2017 13:46 |
Last Modified: | 02 Jan 2018 01:38 |
Published Version: | https://doi.org/10.1016/j.mbs.2016.12.009 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.mbs.2016.12.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:110251 |