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May  2005, 5(2): 335-352. doi: 10.3934/dcdsb.2005.5.335

Intratrophic predation in a simple food chain with fluctuating nutrient

S. R.-J. Jang 1, , J. Baglama 2, and  P. Seshaiyer 3,

1. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States
2. 

Department of Mathematics, University of Rhode Island, Kingston, RI 02881, United States
3. 

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, United States

Received  March 2003 Revised  March 2004 Published  February 2005

A model of interaction between nutrient, prey, and predator with intratrophic predation of the predator and a limiting periodic nutrient input is proposed and studied. Dynamics of the system are shown to depend on two thresholds. These thresholds are expressed in terms of certain periodic solutions of the system. Intratrophic predation can have impact on the model only if both thresholds are greater than zero. In this case positive periodic solutions exist. Numerical techniques are then used to explore the effect of intratrophic predation by examining the mean value and stability of these positive periodic solutions. It is demonstrated numerically that intratrophic predation can increase the stability region of the positive periodic solutions. It can also elevate the mean values of prey population and decrease the mean values of nutrient concentration for stable positive periodic solutions. Moreover, intratrophic predation can eliminate the chaotic behavior of the system when the degree of intratrophic predation is large enough.
Keywords: uniform persistence., thresholds, Poincaré map, intratrophic predation, Population dynamics.
Mathematics Subject Classification: 92D2.
Citation: S. R.-J. Jang, J. Baglama, P. Seshaiyer. Intratrophic predation in a simple food chain with fluctuating nutrient. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 335-352. doi: 10.3934/dcdsb.2005.5.335
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