Behavior analysis for a size-structured population model with Logistic term and periodic vital rates

Volume 11, Issue 12, pp 1337--1354 http://dx.doi.org/10.22436/jnsa.011.12.05

Publication Date: September 15, 2018 Submission Date: March 07, 2018 Revision Date: August 07, 2018 Accteptance Date: August 10, 2018

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Authors

Rong Liu - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, China. Guirong Liu - School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, China.

Abstract

In this paper, we investigate the large-time behavior of a nonlinear size-structured population model with logistic term and \(T\)-periodic vital rates. We establish the existence of a unique non-negative solution of the given model with the given initial distribution. We prove that there exists at most two \(T\)-periodic non-negative solutions (one of them being the trivial one) of the periodic model associated with the given model. We show that for any initial distribution of population the solution of the given model tends to the nontrivial non-negative \(T\)-periodic solution of the associated model. At last, we give the numerical tests, which are used to demonstrate the effectiveness of the theoretical results in our paper.

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Keywords

• Behavior analysis
• logistic term
• periodic vital rates
• size-structure

MSC

•  35L60
•  74H40
•  92D25

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