Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-03
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We study a Lotka-Volterra type predator-prey model with a transmissible disease in the predator population.
We concentrate on the effect of diffusion and cross-diffusion on the emergence of stationary patterns.
We first show that both self-diffusion and cross-diffusion can not cause Turing instability from the disease-free equilibria.
Then we find that the endemic equilibrium remains linearly stable for the reaction diffusion system without cross-diffusion, while it becomes linearly unstable when cross-diffusion also plays a role in the reaction-diffusion system; hence, the instability is driven solely from the effect of cross-diffusion.
Furthermore, we derive some results for the existence and nonexistence of nonconstant stationary solutions when the diffusion rate of a certain species is small or large.
American Psychological Association (APA)
Zhang, Guohong& Wang, Xiaoli. 2014. Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1013393
Modern Language Association (MLA)
Zhang, Guohong& Wang, Xiaoli. Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1013393
American Medical Association (AMA)
Zhang, Guohong& Wang, Xiaoli. Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1013393
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013393