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Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays

  • *Corresponding author: Yuan Yuan

    *Corresponding author: Yuan Yuan 

This work is supported by NNSF of China (grant No. 12101323), Science and Technology Commission of Shanghai Municipality (STCSM) (grant No. 18dz2271000), Natural Science Foundation of Jiangsu Province of China (grant No. BK20200749), Nanjing University of Posts and Telecommunications Science Foundation (grant No. NY220093)

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  • This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.

    Mathematics Subject Classification: Primary: 92D25, 34D20; Secondary: 47E05.


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  • Figure 1.  (a) Time series of $ V(t) $. (b) Time series of $ P(t) $. (c) Solutions of the system (1.1) go to the boundary equilibrium. (d) Time series of $ p(t,a) $. In the four pictures, the lines $ a,\; b,\; c $ correspond to three different sets of initial values

    Figure 2.  (a) Time series of $ V(t) $. (b) Time series of $ P(t) $. (c) Solutions of the system (1.1) go to the positive steady state when $ \tau_1 = \tau_2 = 0.3 $. (d) Time series of $ p(t,a) $

    Figure 3.  (a) Time series of $ V(t) $. (b) Time series of $ P(t) $. (c) Solutions of the system (1.1) oscillates periodically when $ \tau_1 = \tau_2 = 1.2 $. (d) Time series of $ p(t,a) $

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