AN EFFICIENT AND ACCURATE NUMERICAL SCHEME FOR TURING INSTABILITY ON A PREDATOR-PREY MODEL
- Authors
- Yun, Ana; Jeong, Darae; Kim, Junseok
- Issue Date
- 6월-2012
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Turing instability; ratio-dependent predator-prey; semi-implicit scheme
- Citation
- INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v.22, no.6
- Indexed
- SCIE
SCOPUS
- Journal Title
- INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
- Volume
- 22
- Number
- 6
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/108362
- DOI
- 10.1142/S0218127412501398
- ISSN
- 0218-1274
- Abstract
- We present an efficient and accurate numerical method for solving a ratio-dependent predator-prey model with a Turing instability. The system is discretized by a finite difference method with a semi-implicit scheme which allows much larger time step sizes than those required by a standard explicit scheme. A proof is given for the positivity and boundedness of the numerical solutions depending only on the temporal, but not on the spatial step sizes. Finally, we perform numerical experiments demonstrating the robustness and accuracy of the numerical solution for the Turing instability. In particular, we show that the numerical nonconstant stationary solutions exist.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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