Dynamic analysis of a delayed differential equation for <i>Tropidothorax elegans</i> pests

Tingru Yang; Yuting Ding; Tingru Yang; Yuting Ding

doi:10.3934/era.2023352

Electronic Research Archive

2023, Volume 31, Issue 11: 6947-6963. doi: 10.3934/era.2023352

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Theory article

Dynamic analysis of a delayed differential equation for Tropidothorax elegans pests

Tingru Yang ,
Yuting Ding ^,

College of Science, Northeast Forestry University, Harbin 150040, China

Received: 23 August 2023 Revised: 11 October 2023 Accepted: 15 October 2023 Published: 30 October 2023

In this paper, we establish an infectious disease model of Tropidothorax elegans to study the impact of them on plants. Our model involves the time delay for Tropidothorax elegans to hatch eggs, which is influenced by temperature. Second, we theoretically analyze the existence and the stability of the equilibrium and the normal form near the Hopf bifurcating critical point. Next, we choose three groups of parameters for numerical simulations to verify theoretical analysis of our model. Then, based on numerical simulations, we give bioanalysis which are consistent with the patterns of Tropidothorax elegans pests, such as dying off in large numbers of adults during the winter and one or two generations a year.
- infectious disease model,
- plant diseases and insect pests,
- time delay,
- Hopf bifurcation,
- normal form,
- environment
Citation: Tingru Yang, Yuting Ding. Dynamic analysis of a delayed differential equation for Tropidothorax elegans pests[J]. Electronic Research Archive, 2023, 31(11): 6947-6963. doi: 10.3934/era.2023352

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Abstract

In this paper, we establish an infectious disease model of Tropidothorax elegans to study the impact of them on plants. Our model involves the time delay for Tropidothorax elegans to hatch eggs, which is influenced by temperature. Second, we theoretically analyze the existence and the stability of the equilibrium and the normal form near the Hopf bifurcating critical point. Next, we choose three groups of parameters for numerical simulations to verify theoretical analysis of our model. Then, based on numerical simulations, we give bioanalysis which are consistent with the patterns of Tropidothorax elegans pests, such as dying off in large numbers of adults during the winter and one or two generations a year.

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