Asymptotic analysis of a size-structured cannibalism population model with delayed birth process

Dongxue  Yan; Yu  Cao; Xianlong Fu

doi:10.3934/dcdsb.2016032

Article Contents

2016, Volume 21, Issue 6: 1975-1998. Doi: 10.3934/dcdsb.2016032

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Asymptotic analysis of a size-structured cannibalism population model with delayed birth process

1.
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241
2.
Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241

Received: November 2014

Revised: February 2016

Published: August 2016

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Abstract

In this paper, we study a size-structured cannibalism model with environment feedback and delayed birth process. Our focus is on the asymptotic behavior of the system, particularly on the effect of cannibalism and time lag on the long-term dynamics. To this end, we formally linearize the system around a steady state and study the linearized system by $C_0$-semigroup framework and spectral analysis methods. These analytical results allow us to achieve linearized stability, instability and asynchronous exponential growth results under some conditions. Finally, some examples are presented and simulated to illustrate the obtained stability conclusions.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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