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

Published online by Cambridge University Press:  12 May 2021

PENG YANG
Affiliation:
School of Mathematics, Sun Yat-sen University, Guangzhou 510275, 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, Guangzhou 510275, People’s Republic of China emails: yangp79@mail2.sysu.edu.cn; mcswys@mail.sysu.edu.cn
Corresponding

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.

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