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Turing instability analysis and parameter identification based on optimal control and statistics method for a rumor

Bingxin Li1, Linhe Zhu1

  • 1School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China.

Chaos (Woodbury, N.Y.)
|May 30, 2024
PubMed
Summary
This summary is machine-generated.

This study models rumor propagation dynamics using reaction-diffusion systems. Optimal control methods prove more accurate for parameter identification than statistical approaches, even in complex networks.

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Area of Science:

  • Mathematical Biology
  • Network Science
  • Computational Dynamics

Background:

  • Rumor propagation models are crucial for understanding information diffusion.
  • Reaction-diffusion systems offer a framework for spatial dynamics.
  • Parameter identification is key to validating and applying these models.

Purpose of the Study:

  • To establish a reaction-diffusion system for rumor propagation dynamics.
  • To derive conditions for Turing instability and analyze parameter identification.
  • To compare optimal control and statistical methods for parameter identification.

Main Methods:

  • Development of a reaction-diffusion model with two transmission types.
  • Derivation of equilibrium and Turing instability conditions.
  • Application of variational inequalities for optimal control-based parameter identification.
  • Numerical simulations and statistical pattern identification.
  • Extension of methods to small-world networks.

Main Results:

  • Sufficient and necessary conditions for a positive equilibrium point were established.
  • Turing instability conditions for the equilibrium point were derived and verified numerically.
  • Optimal control-based parameter identification demonstrated superior efficiency and accuracy.
  • Consistent conclusions were obtained when extending to small-world networks.

Conclusions:

  • The reaction-diffusion model effectively captures rumor propagation dynamics.
  • Optimal control provides a robust method for parameter identification in these systems.
  • The findings are applicable to both continuous spaces and complex network structures.