JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 100-110.doi: 10.6040/j.issn.1671-9352.0.2021.179

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Dynamics of the stage-structured population system with two kinds of pulses

LYU Ning   

  1. School of Information Engineering, Key Laboratory of Electronic Commerce Technology and Application, Lanzhou University of Finance and Economics, Lanzhou 730000, Gansu, China
  • Published:2021-11-25

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Abstract: This paper studies the complex dynamics of the stage structure population system with birth pulse and harvest pulse. The discrete dynamical model of the system is determined by stroboscopic mapping, and the existence and stability of the equilibrium point are discussed. The central manifold theory is available to study the period-doubling bifurcation of the equilibrium point. By light of numerical simulation, it is revealed that a series of period-doubling bifurcation cascades connects together to form a Feigen-baum tree link(anti-monotonicity)with the parameters varying. What is the most interesting thing is that the topology of the periodic island formed by these Feigen-baum trees in the two-dimensional parameter space is arranged according to the Stern-Brocot tree instead of the familiar Farey tree.

Key words: population system, eriod doubling bifurcation, Farey tree, chaos

CLC Number: 

  • O441.4
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