Related Experiment Video
Updated: Oct 28, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Stochastic Rumor Propagation Dynamics with Log-Normal Ornstein-Uhlenbeck Process
Nafisa Ablat1, Shuzhen Yu1, Haijun Jiang1
1School of Mathematics Science, Xinjiang Normal University, Urumqi 830017, China.
Abstract:
Considering the inevitable impact of environmental interference on rumor propagation, this paper constructs and studies a stochastic rumor propagation model in which the diffusion rate is described by the Log-normal Ornstein-Uhlenbeck (OU) process. Firstly, we rigorously prove the existence and uniqueness of global positive solutions for the model, which serves as a fundamental prerequisite for further dynamical analysis. Subsequently, by constructing an appropriate Lyapunov function and combining it with the ergodic property of the OU process, sufficient criteria for the existence of a stationary distribution of the system are given. Finally, we demonstrate that when R0e≤1, rumors will tend to become extinct at an exponential rate.
Related Concept Videos
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Systematic Error
Entropy Changes Accompanying Specific Processes
Probability Distributions
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Modeling with Differential Equations
Poisson Probability Distribution
The...