Nonlinear Dynamics

, Volume 94, Issue 2, pp 827–844 | Cite as

Mode change in the dynamics of exploited limited population with age structure

  • G. P. Neverova
  • A. I. Abakumov
  • I. P. Yarovenko
  • E. Ya. Frisman
Original Paper


This study focuses on the dynamics of exploited limited population with age structure and compares dynamic modes of population models with and without exploitation while considering age-specific harvesting. Transcritical, period-doubling, and Neimark–Sacker bifurcations occur in the population models. In the case of juvenile harvest, the way of stability loss does not depend on the harvest rate. However, in the case of adult harvest, the hydra effect occurs, which is an increase in harvest rate that subsequently increases the stationary size of the young group. As a rule, harvesting leads to dynamics stabilization. However, the models reveal multistability. Hence, in the case of exploitation, different dynamic modes can occur with their attraction basins at the same population parameter values. Irregular harvesting or a changing harvest rate may also result in fluctuations in exploited population size because the current population size can shift from one attraction basin to another. Controlling exploited population dynamics is sufficient to shift and retain the population number to within the attraction basin of the dynamic mode selected.


Population dynamics Age-specific harvest Mathematical modeling Dynamics modes Bifurcations Multistability Attraction basins 



This work was partially supported by the Russian Foundation for Basic Research (No. 15-29-02658 ofi_m).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


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Authors and Affiliations

  • G. P. Neverova
    • 1
    • 2
  • A. I. Abakumov
    • 1
    • 3
  • I. P. Yarovenko
    • 3
    • 4
  • E. Ya. Frisman
    • 2
  1. 1.Institute of Automation and Control Processes of the FEB RASVladivostokRussia
  2. 2.Institute for Complex Analysis of Regional Problems of the FEB RASBirobidzhanRussia
  3. 3.Far Eastern Federal UniversityVladivostokRussia
  4. 4.Institute for Applied Mathematics of the FEB RASVladivostokRussia

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