Special Issue: Dynamical systems and their applications: theoretical analysis and data-driven methods

Guest Editors

Prof. Yanhui Guo
Department of Computer Science, University of Illinois Springfield, Springfield, IL 62703, USA
Email: yguo56@uis.edu

Prof. Liang Kong
Department of Mathematical Sciences and Philosophy, University of Illinois Springfield, Springfield, IL 62703, USA
Email: lkong9@uis.edu

Prof. Shuwen Xue
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
Email: sxue@niu.edu

Manuscript Topics

Dynamical systems theory provides a powerful framework for understanding the behavior and evolution of complex phenomena in various scientific disciplines, including physics, biology, chemistry, and atmospheric science. Notably, many of these dynamical systems possess an exceptionally high-dimensional state space, characterized by dynamics that span a wide range of both temporal and spatial scales. Consequently, these systems present formidable challenges for analytical analysis and numerical simulation. Recent advances in computing power and artificial intelligence have opened new possibilities for integrating theoretical and data-driven techniques when analyzing these models. This proposed special issue aims to explore the synergy between theoretical analysis and data-driven methods in the context of complex dynamical systems and their applications. By bringing together experts from diverse fields, we aim to deepen our understanding of complex processes and enhance the predictive capabilities of dynamical systems models.

We invite original research contributions that address a wide range of topics, including but not limited to:
• Theoretical analysis of ODE and PDE
• Data-driven modeling methods of model reduction
• Models for chemotactic movements and infectious diseases
• Scientific Machine Learning methods in dynamical system
• Artificial Intelligence-empowered biological image/video processing and recognition

We particularly welcome studies integrating theoretical mathematics and data-driven approaches when working with differential equation models. Both original research and comprehensive surveys will be considered for this special issue. All submitted manuscripts will be reviewed promptly and thoughtfully, with authors receiving timely feedback.

Dynamical Systems, Differential Equations, Partial Differential Equations, Data-driven modeling, Scientific Machine Learning, Biological Image Processing

Instructions for authors
Please submit your manuscript to online submission system

Paper Submission

All manuscripts will be peer-reviewed before their acceptance for publication. The deadline for manuscript submission is 31 August 2025

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