Dear Colleagues,

The Special Issue “Recent Advances in Spatio-Temporal Dynamics of Differential Equations” aims to bring together researchers and practitioners from all scientific backgrounds to contribute their original research articles and reviews. It is well known that differential equations have long been playing a crucial role in a wide range of scientific disciplines, both theoretically and practically. In return, natural sciences of all branches have been a constant source of many intriguing and challenging problems in the theory and applications of differential equations. Over the past few decades, the scientific community has witnessed an exponentially growing interest in spatio-temporal patterns observed in numerous complex systems that are the primary focus of many interdisciplinary fields due to the profound implications of these patterns. Meanwhile, differential equations, as a mathematical tool, have consistently and significantly contributed a better understanding of the underlying mechanisms of complex systems that stem from biology, engineering, physics, medicine, and other scientific fields that are becoming increasingly quantitative and more reliant on mathematical approaches. To reflect on the latest achievements and present ongoing challenges, this Special Issue aims to summarize and highlight the current state-of-the-art progress in the studies of spatio-temporal dynamics of differential equations. It welcomes both theoretical and application-oriented contributions across all spectrums of the theory and applications of differential equations, including, but not limited to:

1. Asymptotic behavior of solutions of differential equations and difference equations;
2. Self-similar solutions and traveling wave solutions of differential equations;
3. The applications of nonlinear topological methods in differential equations;
4. Spatio-temporal dynamics of reaction–diffusion equations and nonlocal diffusion equations;
5. Numerical methods of differential equations and their applications;
6. Mathematical modeling in biology and epidemiology.

The Special Issue seeks to showcase and stimulate the productive interplay between theoretical studies and practical applications. As emerging challenges could inspire novel ideas and nourish the next generation of scientists, it is the ultimate goal of this Special Issue to promote and foster interdisciplinary collaborations.

Dr. Guangyu Zhao
Dr. He Zhang
Guest Editors

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• spatio-temporal dynamics
• propagation phenomena
• asymptotic behavior
• topological methods
• numerical methods
• mathematical modeling