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Periodic trajectories for an age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion

Part of: Infinite-dimensional dissipative dynamical systems Parabolic equations and systems

Published online by Cambridge University Press:  12 May 2021

PENG YANG Open the ORCID record for PENG YANG [Opens in a new window]  and
YUANSHI WANG
PENG YANG
Affiliation:
School of Mathematics, Sun Yat-sen University, Guangzhou510275, People’s Republic of China emails: yangp79@mail2.sysu.edu.cn; mcswys@mail.sysu.edu.cn
YUANSHI WANG
Affiliation:
School of Mathematics, Sun Yat-sen University, Guangzhou510275, People’s Republic of China emails: yangp79@mail2.sysu.edu.cn; mcswys@mail.sysu.edu.cn
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Abstract

This paper studies the periodic trajectories of a novel age-structured prey–predator system with Michaelis–Menten functional response including delays and asymmetric diffusion. To begin with, the system is turned into an abstract non-densely defined Cauchy problem, and a time-lag effect in their interaction is investigated. Next, we acquire that this system appears a periodic orbit near the positive steady state by employing the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, which is also the main result of this article. Finally, in order to illustrate our theoretical analysis more vividly, we make some numerical simulations and give some discussions.

Keywords

Periodic trajectoriesage structureMichaelis–Menten functional responsedelaysasymmetric diffusion

MSC classification

Secondary: 35K90: Abstract parabolic equations 37L15: Stability problems 92D25: Population dynamics (general)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 4 , August 2022 , pp. 587 - 605
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

†

This work was supported by NSF of P.R. China (12071495, 11571382).

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