Spatiotemporal Dynamics of a Predator-Prey System with Linear Harvesting RateReport as inadecuate

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Mathematical Problems in Engineering - Volume 2014 2014, Article ID 625973, 9 pages -

Research ArticleDepartment of Mathematics Education, Catholic University of Daegu, Gyeongsan, Gyeongbuk 712-702, Republic of Korea

Received 11 January 2014; Revised 17 March 2014; Accepted 18 March 2014; Published 7 April 2014

Academic Editor: Asier Ibeas

Copyright © 2014 Hunki Baek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate a spatial ratio-dependent predator-prey system with linear harvesting rate. Byusing linear stability and bifurcation analysis, we obtain the conditions for Hopf and Turing bifurcation in thespatial domain. In addition, we classify spatial pattern formations of the system by making use of numericalsimulations. In fact, the numerical simulations unveil that the typical Turing patterns, such as spotted, spot-stripelikemixtures and stripelike patterns, can be observed even if the system has the linear harvesting rate. Inorder to analyze these patterns via the spatial frequency, the discrete Fourier transform is used. Moreover, wediscuss that the linear harvesting system is more realistic than a predator-prey system with constant harvesting. Our results disclose that the spatially extended system with linear harvesting rate has more complex dynamicpatterns in the two-dimensional space. It may help to understand the effects of harvesting on species in the realworld.

Author: Hunki Baek



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