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Research on Dynamical Systems and Differential Equations, 2nd Edition

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Special Issue Editors

Special Issue Information

Dear Colleagues,

Dynamical systems and differential equations are fundamental areas of mathematics that have been applied across a wide range of fields, including physics, chemistry, engineering, biology, economics, electronics, ecology, epidemiology, neural networks, and many other real-world domains. Dynamical systems refer to a collection of mathematical models that describe the time evolution of physical or abstract systems. Differential equations, on the other hand, are mathematical equations that describe the relationship between a function and its derivatives.

Overall, dynamical systems and differential equations comprise a vibrant and active field with numerous applications and exciting open problems.

Therefore, this Special Issue aims to collate findings of mathematicians, biologists, physicists, epidemiologists, engineers, economists, ecologists, mechanists, and other scientists for whom dynamical systems and differential equations are valuable research tools.

Dr. Ahmadjan Muhammadhaji
Dr. Maimaiti Yimamu
Guest Editors

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Keywords

differential equations
deterministic and stochastic differential equations
dynamical systems
modeling and dynamics in population dynamical systems
complex networks
neural networks
epidemic models
disease modeling
stochastic processes and their applications
statistical models and algorithms
stochastic models in biology

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Research

31 pages, 521 KB

Open AccessArticle

Bayesian Analysis of Nonlinear Quantile Structural Equation Model with Possible Non-Ignorable Missingness

by Lu Zhang and Mulati Tuerde

Mathematics 2025, 13(19), 3094; https://doi.org/10.3390/math13193094 - 26 Sep 2025

Abstract

This paper develops a nonlinear quantile structural equation model via the Bayesian approach, aiming to more accurately analyze the relationships between latent variables, with special attention paid to the issue of non-ignorable missing data in the model. The model not only incorporates quantile regression to examine the relationships between latent variables at different quantile levels but also features a specially designed mechanism for handling missing data. The non-ignorable missing mechanism is specified through a logistic regression model, and a combined method of Gibbs sampling and Metropolis–Hastings sampling is adopted for missing value imputation, while simultaneously estimating unknown parameters, latent variables, and parameters in the missing data model. To verify the effectiveness of the proposed method, simulation studies are conducted under conditions of different sample sizes and missing rates. The results of these simulation studies indicate that the developed method performs excellently in handling complex data structures and missing data. Furthermore, this paper demonstrates the practical application value of the nonlinear quantile structural equation model through a case study on the growth of listed companies, providing researchers in related fields with a new analytical tool. Full article

(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations, 2nd Edition)

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