Stability Switching in Lotka-Volterra and Ricker-Type Predator-Prey Systems with Arbitrary Step Size
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Description
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two-species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time discretisation, we obtain stability conditions that preserve the characteristics of continuous-time models and their numerically approximated systems. Here, we show that even small changes to some of the model parameters may alter the system dynamics unless an appropriate time discretisation is chosen to return similar dynamical behaviour to what is observed in the corresponding continuous-time system. We also found similar dynamical properties of the Ricker-type predator-prey systems under certain conditions. Our results demonstrate the need for preliminary analysis to identify which dynamical properties of approximated discretised systems agree or disagree with the corresponding continuous-time systems.
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| ID Code: | 246336 | ||||||||
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| Item Type: | Contribution to Journal (Journal Article) | ||||||||
| Refereed: | Yes | ||||||||
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| Measurements or Duration: | 14 pages | ||||||||
| Keywords: | ecological models, Jacobian matrix, stability conditions, step size, time discretisation | ||||||||
| DOI: | 10.3390/axioms12040390 | ||||||||
| ISSN: | 2075-1680 | ||||||||
| Pure ID: | 162617676 | ||||||||
| Divisions: | Current > Research Centres > Centre for Data Science Current > QUT Faculties and Divisions > Faculty of Science Current > Schools > School of Mathematical Sciences |
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| Funding Information: | K.J.H. acknowledges support from the Australian Research Council Fellowship DE200101791. | ||||||||
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| Copyright Owner: | © 2023 by the authors | ||||||||
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||||||
| Deposited On: | 12 Feb 2024 23:36 | ||||||||
| Last Modified: | 29 Feb 2024 14:17 |
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