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《Journal of Jiangxi Normal University(Natural Sciences Edition)》 2009-03
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Stability and Hopf Bifurcation Analysis for a Nonlinear Differential Equation Model System with Time Delay

LIU Hua-xiang1,ZENG Guang-hong2,WU Qing-chu2 (1.Department of Mathematics,Guangdong Ocean University,Zhanjiang Guangdong 524088,China;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China)  
A nonlinear two-dimensional time-delayed differential equation model system for two competitive phytoplankton species is considered.Firstly the local stability of positive equilibrium point for the non-delayed model system is discussed.Then local stability of positive equilibrium point and Hopf-Bifurcation analysis for the delayed model system is analysed by using Hopf-Bifurcation theory.Local Hopf-Bifurcation is existed as the time delay exceed a threshold value.Finally numerical simulations are carried out to illustrate the analytical result.This model system can capture the oscillatory behavior usually exhibited by various phytoplankton species on a proper parametric value and it is useful for controlling deleterious phytoplanktons.
【Fund】: 广东海洋大学科研(0612163);; 江西师范大学青年成长基金(20071978)资助项目
【CateGory Index】: O175.14
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【Citations】
Chinese Journal Full-text Database 1 Hits
1 ZENG Guang-hong1,LIU Hua-xiang2,WU Qing-chu1(1.College of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China2.College of Science,Guangdong Ocean University,Zhanjiang 524088,China);Normal Form Realization Automatically by Computer[J];Journal of Nanchang University(Natural Science);2008-02
【Co-citations】
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1 LIU Jin-chuan et al(College of Landscape Architecture and Tourism,Hebei Agricultural University,Baoding,Hebei 071001);Study on Agricultural Science and Technology Park Based on Population Ecology[J];Journal of Anhui Agricultural Sciences;2010-26
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3 GAN Nai-feng~(1,2),ZHANG Qing-ling~1,ZHAO Li-chun~2(1.College of Scienences,Northeastern University,Shenyang Liaoning 110006 China;2.Anshan Normal University,Anshan Liaoning 114005,China);Global Struture Analysis of a Kind of Lotka-Volterra System[J];Journal of Anshan Normal University;2006-04
4 Guo Yanfen(Beijing Polytechnic College,Beijing 100042,China);Stability Analysis of a Prey-Predator System[J];Journal of Beijing Polytechnic College;2011-04
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