Hybrid control of Turing instability and Hopf bifurcation in CDK1-APC feedback systems with diffusion

Luan, Yifeng; Xiao, Min; Wang, Zhen; Zhao, Jing

doi:10.1016/j.jfranklin.2023.09.036

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2024

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Cited by 3 publications

References 35 publications

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Pattern Dynamics Optimization of the Schnakenberg System Based on State Feedback Control Strategy

Dong,

Chen,

Xiao

et al. 2024

2024 36th Chinese Control and Decision Conference (CCDC)

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Pattern Dynamics Optimization of the Schnakenberg System Based on State Feedback Control Strategy

Dong,

Chen,

Xiao

et al. 2024

2024 36th Chinese Control and Decision Conference (CCDC)

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Research on parameter identification of an epidemic-like network system based on optimization theory

Zhu,

Chen,

Shen

2024

Eur. Phys. J. Plus

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Investigation of Spatial Pattern in SI Model with PD Control and Cross-Diffusion

Lu,

Yao,

Huang

et al. 2024

Int. J. Bifurcation Chaos

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Spatial patterns are an important characteristic of ecological epidemic reaction–diffusion models, as they help predict the spatial dynamics of epidemic spread. However, there is currently a significant shortage in research on control strategies for generating and regulating these patterns. In this paper, we establish a Susceptible–Infectious (SI) model with Proportional-Derivative (PD) control and cross-diffusion. We analyze the stability of the model without diffusion and provide the conditions for Turing instability driven by diffusion. Using the cross-diffusion coefficient as the bifurcation parameter, we derive the amplitude equation of the two-dimensional Turing pattern at the Turing bifurcation threshold based on the multiple scale method, which determines the selection and stability of pattern formation. Numerical simulations in two-dimensional space show that the bifurcation parameter varies with changes in control parameters, and the PD control not only effectively alters the structure of Turing patterns but also suppresses Turing instability. Furthermore, it is found that more complex spatial patterns in three-dimensional space emerge under PD control.

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Hybrid control of Turing instability and Hopf bifurcation in CDK1-APC feedback systems with diffusion

Cited by 3 publications

References 35 publications

Pattern Dynamics Optimization of the Schnakenberg System Based on State Feedback Control Strategy

Pattern Dynamics Optimization of the Schnakenberg System Based on State Feedback Control Strategy

Research on parameter identification of an epidemic-like network system based on optimization theory

Investigation of Spatial Pattern in SI Model with PD Control and Cross-Diffusion

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