IMPACT OF THE SAME DEGENERATE ADDITIVE NOISE ON A COUPLED SYSTEM OF FRACTIONAL SPACE DIFFUSION EQUATIONS

In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka–Volterra system from biology and the Brusselator model for the Belousov–Zhabotinsky chemical reaction from chemistry to illustrate our results.

Internet Public Opinion Diffusion Mechanism in Public Health Emergencies: Based on Entropy Flow Analysis and Dissipative Structure Determination

As an empirical case, this study selected the illegal production process incidents of rabies and DPT (Diphtheria, Pertussis, Tetanus) vaccines by Changchun Longevity Biotechnology Co., Ltd., which occurred in July 2018. Based on the four factors involved in the spread of public opinion, the public health emergency, netizen, network media, and government, Brusselator model, and entropy method were applied to calculate the positive and negative entropy—to verify whether the Internet public opinion system is a dissipative structure. This study verified four evolution mechanisms in Internet public opinion diffusion, among which the trigger point of entropy-control occurred in the germination mechanism, the entropy-controlled disposal point occurred in the outbreak and fluctuating mechanism, and then became latency in the elimination mechanism. It provides a theoretical reference for the government to judge the stage of such diffusion and improve the governance ability of the opinion mentioned above.

Spatio-temporal Brusselator Model and Biological Pattern Formation

This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.