Research has shown that long non-coding RNAs (lncRNAs) are involved in the regulation of essential biological processes at multiple levels. However so far, the mechanisms of gene expression regulation by lncRNAs and their biological functions are not yet fully understood. This study focuses on the differences in gene expression regulation by lncRNAs through cis-and trans-regulation and their dynamic behaviors. First, a mathematical model for the functional action of lncRNAs is established based on chemical master equations, and the accuracy of the SSA and FSP algorithms is validated. Second, the distribution of lncRNAs and the effect of transcriptional bursts on gene expression are analyzed using SSA and FSP algorithms. This paper combines dynamical system theory and stochastic simulation methods to first construct the model of lncRNA regulatory mechanisms based on experimental results; Then some key indicators ( such as the probability distribution, mean, and noise of mRNA) are then calculated to analyze the dynamic properties exhibited by lncRNAs in cis-and trans-regulation. The study shows that under the original model, trans-regulation leads to higher mRNA expression levels and lower noise, while cis-regulation is more sensitive to rapid local responses. The impact of the lncRNA generation distribution on the dynamic characteristics of mRNA expression is also studied, and it is found that different distribution forms significantly affect the stability and efficiency of the regulatory pattern. After adding transcriptional bursts, cisregulation results in higher average mRNA expression levels and lower noise compared to trans-regulation. This study provides theoretical support for a comprehensive understanding of lncRNA regulatory mechanisms and their functional characteristics in gene expression, offering a new perspective for exploring lncRNA regulatory mechanisms.