Research on pattern dynamics of a class of predator-prey model with interval biological coefficients for capture

Xiao-Long Gao; Hao-Lu Zhang; Xiao-Yu Li; Xiao-Long Gao; Hao-Lu Zhang; Xiao-Yu Li

doi:10.3934/math.2024901

AIMS Mathematics

2024, Volume 9, Issue 7: 18506-18527. doi: 10.3934/math.2024901

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Research article

Research on pattern dynamics of a class of predator-prey model with interval biological coefficients for capture

1.
Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
2.
CCCC Comprehensive planning and Design Institute Co., Ltd, Beijing 100024, China
3.
College of Date Science and Application, Inner Mongolia University of Technology, Hohhot 010080, China
4.
School of Civil Engineering, Inner Mongolia University of Technology, Hohhot 010051, China

Received: 05 April 2024 Revised: 03 May 2024 Accepted: 13 May 2024 Published: 03 June 2024
MSC : 65L10, 65R20

Due to factors such as climate change, natural disasters, and deforestation, most measurement processes and initial data may have errors. Therefore, models with imprecise parameters are more realistic. This paper constructed a new predator-prey model with an interval biological coefficient by using the interval number as the model parameter. First, the stability of the solution of the fractional order model without a diffusion term and the Hopf bifurcation of the fractional order $ \alpha $ were analyzed theoretically. Then, taking the diffusion coefficient of prey as the key parameter, the Turing stability at the equilibrium point was discussed. The amplitude equation near the threshold of the Turing instability was given by using the weak nonlinear analysis method, and different mode selections were classified by using the amplitude equation. Finally, we numerically proved that the dispersal rate of the prey population suppressed the spatiotemporal chaos of the model.
- interval biological coefficient,
- fractional predator-prey model,
- weakly nonlinear analysis,
- Hopf bifurcation
Citation: Xiao-Long Gao, Hao-Lu Zhang, Xiao-Yu Li. Research on pattern dynamics of a class of predator-prey model with interval biological coefficients for capture[J]. AIMS Mathematics, 2024, 9(7): 18506-18527. doi: 10.3934/math.2024901

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Abstract

Due to factors such as climate change, natural disasters, and deforestation, most measurement processes and initial data may have errors. Therefore, models with imprecise parameters are more realistic. This paper constructed a new predator-prey model with an interval biological coefficient by using the interval number as the model parameter. First, the stability of the solution of the fractional order model without a diffusion term and the Hopf bifurcation of the fractional order $ \alpha $ were analyzed theoretically. Then, taking the diffusion coefficient of prey as the key parameter, the Turing stability at the equilibrium point was discussed. The amplitude equation near the threshold of the Turing instability was given by using the weak nonlinear analysis method, and different mode selections were classified by using the amplitude equation. Finally, we numerically proved that the dispersal rate of the prey population suppressed the spatiotemporal chaos of the model.

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