Two different approaches for parameter identification in a spatial–temporal rumor propagation model based on Turing patterns

Abstract

The reaction–diffusion model can well describe the dynamics of groups in space and time to help us to study their behavioral mechanism. Based on the rumor propagation process, an example of reaction–diffusion model defined on continuous space is proposed in this paper to study some common problems under Turing instability. Firstly, the necessary conditions for Turing instability are studied. Furthermore, the amplitude equation of the system is derived through multi-scale analysis and weak linear analysis, and the theoretical conditions for the appearance of hexagon pattern, stripe pattern and mixed structure pattern near Turing bifurcation are given. In the numerical simulation, we verify the correctness of the theoretical analysis and find that the cross-diffusion coefficient can change the pattern type. Finally, based on a statistical method and a convolutional neural network, we have carried out a parameter identification experiment of the system respectively. The results show that the second method performs well and the first method has relatively large error in some cases.