American Institute of Mathematical Sciences

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August  2004, 4(3): 629-634. doi: 10.3934/dcdsb.2004.4.629

Allee effect and a catastrophe model of population dynamics

Dianmo Li 1, , Zhen Zhang 1, , Zufei Ma 1, , Baoyu Xie 1, and  Rui Wang 1,

1. 

The National Laboratory of Integrated Management of Insect and Rodent Pests in Agriculture, Institute of Zoology, Chinese Academy of Sciences Beijing 100080, China, China

Received  November 2002 Revised  February 2004 Published  May 2004

Some assumptions of Logistic Equation are frequently violated. We applied the Allee effect to the Logistic Equation so as to avoid these unrealistic assumptions. Following basic principles of Catastrophe theory, this new model is identical to a Fold catastrophe type model. An ecological interpretation of the results is provided.
Keywords: catastrophe theory, Logistic Equation., Allee effect.
Mathematics Subject Classification: 92D25, 92D4.
Citation: Dianmo Li, Zhen Zhang, Zufei Ma, Baoyu Xie, Rui Wang. Allee effect and a catastrophe model of population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 629-634. doi: 10.3934/dcdsb.2004.4.629
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