Abstract
This paper investigates a predator–prey model with age structure and two delays. By formulating the age-structured model with delays as a non-densely defined Cauchy problem and applying the theory of integrated semigroup and recently established Hopf bifurcation theory for abstract Cauchy problems with non-dense domain, we show that Hopf bifurcation occurs in the model. This also shows the sensitivity of the model dynamics on the threshold \(\tau \) which might be taken as a measure of a biological maturation period and a time lag between conception and birth. Numerical simulations are performed to illustrate the obtained results and a summary is given.
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We would like to thank the Referees for their valuable comments and suggestions that greatly improve the presentation of this work.
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Communicated by Philip K. Maini.
Zhihua Liu: Research was partially supported by NSFC, and Laboratory of Mathematics and Complex Systems, Ministry of Education.
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Liu, Z., Li, N. Stability and Bifurcation in a Predator–Prey Model with Age Structure and Delays. J Nonlinear Sci 25, 937–957 (2015). https://doi.org/10.1007/s00332-015-9245-x
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DOI: https://doi.org/10.1007/s00332-015-9245-x