Special Issue "Recent Advances in Spatio-Temporal Dynamics of Differential Equations"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 31 March 2024 | Viewed by 1456

Special Issue Editors

Dr. Guangyu Zhao
E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of Nevada, 1664 N Virginia St., Reno, NV 89557, USA
Interests: partial differential equations; mathematical biology
Dr. He Zhang
E-Mail Website
Guest Editor
College of Mathematics, Jilin University, Changchun 130012, China
Interests: differential equations; dynamic systems

Special Issue Information

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


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

Published Papers (1 paper)

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Spatiotemporal Dynamics of Reaction–Diffusion System and Its Application to Turing Pattern Formation in a Gray–Scott Model
Mathematics 2023, 11(6), 1459; https://doi.org/10.3390/math11061459 - 17 Mar 2023
Cited by 6 | Viewed by 1217
This paper deals with the effects of partial differential equations on the development of spatiotemporal patterns in reaction–diffusion systems. These systems describe how the concentration of a certain substance is distributed in space or time under the effect of two phenomena: the chemical [...] Read more.
This paper deals with the effects of partial differential equations on the development of spatiotemporal patterns in reaction–diffusion systems. These systems describe how the concentration of a certain substance is distributed in space or time under the effect of two phenomena: the chemical reactions of different substances into some other product and the diffusion which results in the dispersion of a certain substance over a surface in space. Mathematical representation of these types of models are named the Gray–Scott model, which exhibits the formation of patterns and morphogenesis in living organisms, e.g., the initial formation of patterns that occur in cell development, etc. To explore the nonhomogeneous steady-state solutions of the model, we use a novel high-order numerical approach based on the Chebyshev spectral method. It is shown that the system is either in uniform stabilized steady states in the case of spatiotemporal chaos or lead to bistability between a trivial steady state and a propagating traveling wave. When the diffusion constant of each morphogen is different in any two species of the reaction–diffusion equation, diffusion-driven instability will occur. For the confirmation of theoretical results, some numerical simulations of pattern formation in the Gray–Scott model are performed using the proposed numerical scheme. Full article
(This article belongs to the Special Issue Recent Advances in Spatio-Temporal Dynamics of Differential Equations)
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