Analysis of a Chemotaxis Model with Nonlinear Production Terms in Wheat Pest Control

Xiangshao Meng; Peilin Xu; Wei Wang; Shilong Luo; Yan Zhang; Xingkai Liu

doi:10.62051/ijafsr.v4n1.01

Authors

Xiangshao Meng
Peilin Xu
Wei Wang
Shilong Luo
Yan Zhang
Xingkai Liu

DOI:

https://doi.org/10.62051/ijafsr.v4n1.01

Keywords:

Logistic source, Chemotaxis, Nonlinear production term, Boundedness

Abstract

Chemotaxis refers to the influence of chemical substances in the environment on the movement of motile species and serves as an important mechanism of cellular communication. Cells communicate with each other by secreting chemical substances, which in turn determine their movement and differentiation. In order to better understand the growth patterns and aggregation distribution of biological populations, an increasing number of scientists have begun to study chemotaxis and describe the observed phenomena by establishing mathematical models. Among these models, the most classical one is the Keller–Segel chemotaxis model. The first part of this paper mainly introduces the development process and current research status of chemotaxis models related to the content of this study, and provides a general overview of the main topics investigated in this paper. The second part of this paper, namely Chapter 2, studies the following chemotaxis mode (which is a parabolic–parabolic–elliptic system with nonlinear production terms and a Logistic-type source). We analyze the global boundedness of its solutions, where is a bounded domain and the system is subject to Neumann boundary conditions. Here, the nonlinear production terms of the attractive and repulsive chemical substances are described by and respectively. Moreover, the Logistic source in this model satisfies Finally, it is concluded that if that is, when either the Logistic source or the repulsive term dominates the attractive term, the solution is globally bounded. Moreover, in the three balanced cases or the boundedness of the solution depends on the magnitude of the corresponding coefficients. The third part of this paper mainly summarizes the main results of the study and provides a preliminary outlook on future research on chemotaxis models with nonlinear production terms.

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