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Dynamics of a delayed population patch model with the dispersion matrix incorporating population loss

Part of: Functional-differential and differential-difference equations Applications - Dynamical systems and ergodic theory

Published online by Cambridge University Press:  21 March 2023

Dan Huang  and
Shanshan Chen Open the ORCID record for Shanshan Chen [Opens in a new window]
Dan Huang
Affiliation:
School of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, P.R. China
Shanshan Chen*
Affiliation:
Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong, 264209, P.R. China
*
*Correspondence author. Email: chenss@hit.edu.cn
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Abstract

In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate is smaller than a critical value. The stability of the positive equilibrium and associated Hopf bifurcation are investigated when the dispersal rate is small or near the critical value. Moreover, we show the effect of network topology on Hopf bifurcation values for a delayed logistic population model.

Keywords

Hopf bifurcationpatch structuredelaypopulation loss

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 34K18: Bifurcation theory 34K13: Periodic solutions 37N25: Dynamical systems in biology
Type
Papers
Information
European Journal of Applied Mathematics , Volume 34 , Issue 4 , August 2023 , pp. 870 - 895
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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