Recent Advances in Nonlinear Dynamics: Chaos, Synchronization, and Their Theoretical and Practical Applications

Dear Colleagues,

Nonlinear dynamics is a fundamental field of study that explores complex behaviors in physical, biological, and engineered systems. Among its most intriguing phenomena are chaos—when deterministic systems exhibit extreme sensitivity to initial conditions—and synchronization—when coupled systems adjust their rhythms to achieve coordinated behavior. Investigation of these concepts, along with related theories such as bifurcations, fractals, and pattern formation, has led to significant breakthroughs in our understanding of real-world systems. The development of new analytical and computational tools continues to deepen our grasp of nonlinear dynamics, making it a vibrant area of research with far-reaching implications.

The aim of this Special Issue is to highlight recent advances in nonlinear dynamics, particularly in chaos theory, synchronization mechanisms, and their applications across diverse disciplines. Contributions may include theoretical studies on stability, control strategies for chaotic systems, novel synchronization schemes in networks, and data-driven approaches for identifying nonlinear dynamics in real-world data. Additionally, emerging topics such as machine learning for nonlinear systems, fractional-order dynamics, and quantum chaos are of great interest. By bringing together cutting-edge research, this collection seeks to foster new methodologies and interdisciplinary connections that push the boundaries of nonlinear science.

We welcome original research and review articles on all aspects of nonlinear dynamics, including but not limited to chaotic oscillators, synchronization in complex networks, nonlinear waves, Hamiltonian systems, and applications in physics, biology, engineering, and climate science. Studies involving experimental validations, numerical simulations, or analytical techniques are encouraged. The published works will not only advance theoretical understanding but also inspire innovative applications in control systems, secure communications, neural networks, and beyond. Through this Special Issue, we hope to stimulate further exploration of nonlinear phenomena and their transformative potential across science and technology.

Dr. Runfa Zhang
Prof. Dr. Zhongzhou Lan
Dr. Jianguo Liu
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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.