Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage

JIA Xibei; LIN Xiaolin; LI Jianquan; CAO Meiqi

doi:10.21656/1000-0887.430120

Volume 44 Issue 3

Mar. 2023

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JIA Xibei, LIN Xiaolin, LI Jianquan, CAO Meiqi. Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage[J]. Applied Mathematics and Mechanics, 2023, 44(3): 355-366. doi: 10.21656/1000-0887.430120

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Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage

doi: 10.21656/1000-0887.430120

School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi’an 710021, P.R.China

Received Date: 2022-04-05
Accepted Date: 2022-08-01
Rev Recd Date: 2022-06-06

Available Online: 2023-02-21

Publish Date: 2023-03-15

Abstract

Abstract

In view of the density dependence of mature individuals, a two-stage cannibalistic model with the egg-to-maturity stage was established. The dynamic behaviors of the model were discussed from two aspects. In the case without cannibalism, the global asymptotic stability of the equilibrium points was proved through construction of the Lyapunov function, while in the case with cannibalism, the existence of saddle-node bifurcation due to cannibalism was proved with the center manifold theorem. Through construction of the Dulac function, nonexistence of the limit cycle in the two-dimensional autonomous system was elucidated, and therefore, the global stability of the equilibrium points was obtained. Finally, the theoretical results were verified through numerical simulation.
- cannibalism,
- saddle-node bifurcation,
- density dependence,
- Dulac function

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References(22)

References

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