American Journal of Computational Mathematics

Volume 6, Issue 2 (June 2016)

ISSN Print: 2161-1203   ISSN Online: 2161-1211

Google-based Impact Factor: 0.42  Citations  

Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

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DOI: 10.4236/ajcm.2016.62014    2,144 Downloads   2,932 Views  Citations
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ABSTRACT

A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.

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Zhang, L. and Zhang, C. (2016) Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate. American Journal of Computational Mathematics, 6, 130-140. doi: 10.4236/ajcm.2016.62014.

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