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Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

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A time independent least squares algorithm for parameter identification of Turing patterns in reaction-diffusion

Lili Chang^1,2, Xinyu Wang^3,4, Guiquan Sun^5,6

¹Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China. changll@amss.ac.cn.

Journal of Mathematical Biology

|November 28, 2023

Summary

We developed a new algorithm to identify parameters in Turing patterns, which are dynamic properties in reaction-diffusion systems. This method is more efficient for complex networks, overcoming limitations of existing approaches.

Keywords:

Least squares Parameter identification Reaction–diffusion systems Time independence Turing patterns

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Area of Science:

Mathematical modeling
Complex systems dynamics
Pattern formation

Background:

Turing patterns are crucial dynamic properties in reaction-diffusion systems (e.g., epidemic, ecology, chemical reactions).
Identifying parameters for Turing patterns in continuous and networked systems is a challenging inverse problem.
Current algorithms are computationally intensive, especially for large-scale complex networks.

Purpose of the Study:

To introduce a novel, efficient algorithm for parameter identification of Turing patterns.
To address the computational limitations of existing methods, particularly for complex network systems.

Main Methods:

Developed a time-independent least squares algorithm based on Turing patterns as stationary solutions.
Transformed the parameter identification problem into a low-dimensional optimization problem.
Utilized low-order linear algebra equations for efficient computation.

Main Results:

Numerical simulations confirmed the algorithm's effectiveness and robustness.
The new method significantly reduces computational resource requirements.
Demonstrated superior performance compared to existing algorithms for reaction-diffusion systems on complex networks.

Conclusions:

The proposed least squares algorithm offers an efficient solution for parameter identification in Turing patterns.
This method is particularly advantageous for large-scale, complex reaction-diffusion systems.
The algorithm provides a computationally feasible approach to a challenging inverse problem.